When talking about positive/negative punishment/reinforcement from a psychological perspective, it can be easy to get tripped up by the emotions around the words themselves.
(You have punishment and reinforcement laid out properly in your question, I'm just adding extra details for future visitors)
The way to look at it is that the positive/negative and punishment/reinforcement are two completely separate categories. Positive/negative indicates how you are trying to change the behavior. Adding something is positive and removing something is negative. Punishment/reinforcement indicates the end goal of the behavior change. Stopping or reducing the behavior would use punishment. Increasing or encouraging the behavior would use reinforcement.
Positive/Negative and punishment/reinforcement are not necessarily good or bad or mean or fair, they just describe how you are trying to adjust the behavior.
When you turn on a car, the car makes annoying beeping sounds until you put on your seat belt. The car is trying to encourage you to wear a seat belt and removes the annoying beep once you do the desired behavior. This is negative (removed beeping) reinforcement (want more seat belt wearing in future).
When a team of employees successfully completes a challenging project, the company throws a party for them. The company is trying to encourage the employees to complete challenging projects and adds the party after the project is successfully completed. This is positive (added party) reinforcement (want more challenging projects completed in future).
When a child throws a tantrum at the playground, the parent takes them home immediately. The parent is trying to discourage the tantrum and removes the child's access to the playground when the tantrum occurs. This is negative (removed playground) punishment (want fewer tantrums in future).
When a driver drives faster than the speed limit, they are given a traffic ticket by a police officer. The officer is trying to discourage breaking the speed rules and adds the traffic ticket when the driver breaks the rules. This is positive (added ticket) punishment (want fewer occurrences of breaking the speed limit).
Applying to your situation
All the various forms of behavior change will work, provided that you are consistent when you enforce them. You also do not need to stick to just one, you can use more than one punishment/reinforcement to affect the same behavior. (In fact, you'll find that most of the time you are naturally doing both a punishment and a reinforcement.) With that said, let's dive into the specific challenge presented here.
We want to discourage Maple from barking at friends and family. Because we want to reduce the barking, this will be a either a positive punishment or negative punishment. It does not need to be mean or vindictive, but it is a punishment nonetheless. Simultaneously, we want to encourage Maple to be calm when friends and family arrive. This will be a reinforcement of the calm behavior.
The effectiveness of the punishment and reinforcement system will depend on what motivates Maple. We have a pug that loves both treats and attention and hates being ignored, but other dogs will vary based on their own personalities, so feel free to substitute the rewards and punishments for whatever works with your own dog. With that said, DO NOT use any sort of physical or verbal abuse as a punishment, it does much more harm than good and teaches your dog to be afraid of you more than anything else.
If Maple is excited to see your visitors and wants to interact or play with them, pick Maple up and take her to another room and don't let her come out until she stops barking. This is negative (removing Maple from the exciting visitors) punishment (want to reduce the barking).
After Maple stops barking, bring her back into the room and allow her to play with the visitors as long as she doesn't bark. This is positive (adding Maple back to the exciting visitors) reinforcement (want to encourage interacting with the visitors calmly, without any barking). If Maple starts to bark again, repeat the punishment until she stops, then bring her back and try again. It may take several cycles for her to understand and break out of old habits, especially if she has been barking before without any consequences.
Eventually, when friends and family arrive and Maple does not bark at all, go all out with the reinforcement. Give treats, praise, petting, ear rubs, tummy rubs, whatever she appreciates the most. (If you don't want to give her too many treats due to her small size, break up a treat into little pieces and give them to her one by one. It makes the single treat seem like more treats, even though the end result is the same total volume of treats eaten.) You want to make it clear as night and day when Maple is doing what you want, and lots of reinforcement the first time she does this correctly will help her link the positive outcome to the behavior. After she is consistently behaving as expected, you can start to lower the reinforcement, and eventually switch to variable rewards, where you give the higher value rewards only periodically. It is still important to provide at least some reinforcement (such as verbal praise or a quick pat) so that Maple keeps up the behavior and doesn't revert to her old ways.
Your fears are correct. You should not give her a treat when she barks at visitors, because that will encourage her to repeat the behavior. You should instead give a treat when she does not bark at friends and family at all.
To use fewer treats, break the treats into smaller pieces. As long as Maple understands that she is getting a reward when she behaves properly, the size of the reward is not as important. (Caveat being that the first few times she behaves properly, you want to lavish her with rewards to really drive the point home). As Maple gets better at understanding what she needs to do, you can decrease and/or randomize the reward and still have her behave.
As long as you are not physically or emotionally harming her (and you seem to be a caring pet parent, so I don't see that as being a problem), the only risk is that you accidentally encourage the wrong behavior. You can always adjust how you set up your rewards and punishments to correct that.
Maple's age does not affect how well this will work. If she has developed a habit of barking at friends and family, it will take longer to break that habit than if she was a new puppy, but she will still get there eventually. Being consistent in applying your rewards and punishments is key. If you only punish her every three times, she will learn that she can bark 2/3rds of the time without consequence.
Alternatives: If Maple is not barking, you can have your friends and family be the ones to give her a treat (replacing the treat you would give her), helping her associate friends and family with good things. It is very important to not give any treats if she barks, you want her to associate the treats with being calm and not barking.