F500 owner here. I would tend to disagree with boxheadtim characterizing a FF as slow. That said, yeah, your laptime isn't made on the straight. Look at laptimes to settle it, I don't want to cause an argument.
You have highlighted a primary struggle for open wheelers. Unless you don't fear death and can find an organization that doesn't fear your death, you won't be mixing with production cars. ( For reference, my head is lower than the doorhandles on my sn95 mustang) For the most part, the narrative is, "bring enough wings and things for your own run group and we will do it". Either that or " we have enough production cars to fill out event, it's not worthwhile for us to consider".
There are groups specific to wings and things that run test days, but most of them are almost invite only and you need a race license.
I am looking at Pennsylvania Hillclimb Association events at Summit Point to get my feet wet with time trials.
Insofar as expense, an F5 isn't bad at all. Buy-in is cheap, maintenance isn't bad at all compared to other club racing legal vehicles. I may rebuild a motor a touch more often than a spec Miata, but it's dirt cheap and easy on a two stroke and the F6 bike motor cars are just a junkyard bike motor (legit runoff wins on salvage motors). Tires last forever (for race tires) due to big tire light light car.
If you don't want to autocross or wheel to wheel, it's not a great fit. I'd consider a legends car or a (well built, big good cage) locost if you want small light cheap speed. The legends car is amazingly affordable and likely where I'd start for a better option down your desired use.
I'd love to get another person into F5, but I don't want you jumping in with your eyes shut.
I will say this. I've autocrossed since 2004 from esp to sts to XP. Anything on street tires was getting boring. The F5 makes my hands shake after a run. Easy FTD unless a decent shifter kart shows in most cases.
Regarding tow vehicle in the case of F5. The car weighs 650lbs without me in it. If you right size an open trailer to the car, very good chance your daily can tow it. Cars are tiny and could fit in a shed.