It looks to me like you're already off to a pretty good start with the topical Broadline treatment and with fumigating your house. I'm not convinced the "pesticide-free all-in-one flea spray" you're using is really doing anything, though, but I haven't tried it myself.
As motosubatsu notes, washing your cat with a flea shampoo might help. Since you say you'll be taking your cat to see a vet anyway, I'd recommend asking them to prescribe a suitable medicated shampoo instead of resorting to over-the-counter products of questionable effectiveness.
Also note that washing your cat within a few days after applying a topical anti-flea treatment like Frontline / Broadline is not recommended, since it may reduce the effectiveness of the treatment. For example, the EPAR for Broadline says:
No data on the effect of bathing/shampooing on the efficacy of the veterinary medicinal product in
cats is available. However, brief contact of the animal with water on one or two occasions within the
month following application is unlikely to significantly reduce its efficacy. As a precaution, it is not
recommended to bathe animals within 2 days after topical treatment.
Note that bathing cats (just like feeding them pills or making them do anything else they don't like) is a game of skill. Your vet may be able to show you the proper technique, so you don't have to learn it by trial and error. Of course, the personality of the cat also matters: some cats are quite tolerant of being bathed, others will literally fight you tooth and claw.
(What worked when I had to wash my own Siberian was setting him in the bathroom sink facing left and holding him there with my left hand's index finger and thumb gently but firmly around his neck while using my right hand to bathe him with warm water from the tap. Do make sure the water really is nice and warm; nobody likes a cold shower, cats least of all. And whatever you do, don't make the mistake of taking your shirt off to keep it from getting wet. Trust me, a wet shirt is far preferable to having a scared and angry cat climb its way straight up the bare skin on your back. Ouch. At least I never tried that technique twice.)
Another option to consider would be trimming your cat's hair (or, perhaps better, having a professional pet groomer do it). Not all the way down to the skin, mind you, but just enough to make the remaining hair easier to clean.
Since you say that the treatments you've already applied are working for your short-haired cat, but not for the long-haired one, temporarily making the long-haired cat's hair shorter would seem like a reasonable approach to try. Especially so if, as you say, your cat "hates being brushed".
Long-haired cats really should have their hair regularly groomed to keep it clean and free of tangles, anyway. If yours doesn't like that, whether it's due to irritation caused by the fleas or for other reasons, trimming their hair might be worth considering.
Again, of course, I'd suggest talking with your vet about all the treatment options you're considering first.
As for your observation of "nervous ticks and skittish behaviour", that could indeed be a side effect of the Broadline treatment, especially if the cat managed to lick off (and thus ingest) some of the product from its hair. The Broadline EPAR linked above says, in section 4.5 ("special precautions for use"; emphasis mine):
It is important to apply the veterinary medicinal product to a skin area where the cat cannot
lick it off: on the neck, in between shoulders. Avoid animals licking each other following
Oral ingestion of the veterinary medicinal product resulted in common to uncommon
vomiting, hyper-salivation and/or in transient neurological signs such as ataxia,
disorientation, apathy and pupil dilation in safety studies. Muscle tremors have been reported
in very rare cases based on post marketing safety experience. These signs usually resolve
spontaneously within 24 hours. On very rare occasions, symptomatic treatment can be
That certainly does seem to match the symptoms you've observed. While the most important way to avoid these symptoms is to do your best to keep your cats from licking the Frontline / Broadline off their own or each other's fur, you could also ask your vet to try prescribing them some other anti-flea treatment that might be better tolerated. Different drugs have different side effects, and just like people, some cats may simply be more sensitive to some drugs than others.
On the other hand, if you can't find any other treatment that is both effective and free of side effects, you may have to just weigh the harm from the side effects against the harm from allowing the flea infestation to persist. Nobody likes to see their pet suffer any kind of bad effects from medical treatment, but suffering from fleas or other parasites isn't pleasant, either. Just like with medicine for people, it's not really a question of whether there are any side effects, but of whether the side effects are worse than the illness the drug is treating.
You should also make sure that your cat isn't getting reinfected with fleas from around your home. The flea bombs and traps are a good start, as is regularly vacuuming your house. (Do remember to take out the vacuum bags regularly, too, to prevent them from acting as flea hatcheries.) I'd also recommend regularly washing (not just spraying) any clothes and bedding that might harbor flea eggs and larvae. Machine washing, especially if followed by tumble drying, should do a good job of killing any fleas and their eggs.
The Flea Science site I linked to above also recommends using an insect growth regulator spray or fumigation product, which should prevent any remaining flea eggs and larvae in your house from maturing into adult fleas, and thus provides long-term protection against the infestation re-emerging.
Pyriproxyfen based IGR products can also be used for outdoor flea control, if you suspect that your cats are picking up fleas from your yard. Typically, you'd want to target the treatment to any shaded spots, e.g. under your porch, that your cats like to hide in. Of course, if your cats roam widely, you may not be able to effectively treat all the spots where they may be picking up fleas.
For long term flea control you may also want to consider installing a dehumidifier in your home. Fleas need a warm and moist environment to grow and survive, and below 50% relative humidity their eggs and larvae will desiccate and die. Unfortunately they like to hide in places, like inside carpets or bedding and under your cats' hair, where the local humidity is higher. Still, if you can keep the ambient humidity in your home consistently well below 50%, that should at least reduce the number of places where flea eggs and larvae can survive.