I guess that the first questions I'd have to ask a fella contemplating a Handi for F Class, is first, do you want to be competitive, and second, are you comfortable paying the match fees on a regular basis to line the pockets of the guy that is going to win the match?
I know there's a mindset in some guys, that says "I'm gonna show these guys that I can keep up with 'em if I had to shoot my Daisy Red Rider", and a good self-opinion is good, but unless you just want to poke some long range shots towards the butts, the Handi just isn't the best platform for this sport.
I attended (within the last month) a 1.000 yard F, F/TG match, and several of the fellas shooting mentioned that they got their starts with heavy barreled 700 Remington .308's, and Bushmaster heavy barrel/fast twist 5.56 rifles. They admitted they spent more on the glass than they did on their rifles. Now, they were shooting AT LEAST, a Tubb bolt gun, or one of the high dollar single shot bolt actions in aluminum stocks with Krieger barrels showing the highest number present. I was asking, because MY 1K experience was with an M14, an iron sighted M1903A3, and a 1903A4 Sniper rifle with a 10X Lyman Target scope. The F Class was a fledgling game back then, mostly for us handicapped types who still wanted to shoot long range, but couldn't keep up with the younger guys who could still use irons and a sling. Nowadays, the F class guys have a 30 pound rifle weight limit, use bipods up front and rear bags, with triggers that go off by themselves in a stiff breeze. They also spent more on their rifles than I did on my F-250!
If a guy wants to spend a lot of money to build a rifle and have fun with it, I'll be the last guy in line to say you shouldn't do it, but it's also a LOT more fun to have gear that will at least give you a sportin' chance at having your name a bit higher on the score sheets.
Good luck, and I hope (sincerely!) that it works out well for You! Please, let us know how it pans out!