For myself, I do/do tighten the filter as per the factory recommendations....2 full turns after gasket first contacts the block.
If you noticed, the threads are quite fine compared to a "normal" filter so you probably need the 2 full turns to make a decent seal. My .02...
As to the oil on the header thing: I let it drain off as much as possible and then take an old oily t-shirt I keep around just for wiping the header down. Then a paper towel lightly moistened with solvent to get the remainder of the oil off, a final wipedown with a clean paper towel and I'm good to go. You've gotta start the engine to fill the filter and check it for leaks and to make sure the oil is circulating properly anyways....and this will burn off any residual oil and/or solvent. Stinks for about 3 - 5 minutes....but I know my header will never rust out.
Lastly: the first special tool I bought for my bike was the proper filter "socket" that fits over the top of the filter itself. On my 3G it's quite easy to get a 3/8" ratchet AND the filter "socket" in behind the header and on to the top of the filter. Gloves are recommended....just in case the header is still a little toasty when you attempt this. The filter "socket" was made by Imperial Eastman and it's their part #IF-6814. I bought it through work but I think they only retail at something like ~$15 which is cheap for a tool that saves so much time and aggro, IMO.
I'm not sure if you 4G 1250 guys can get use a ratchet/"filter socket" combo as easily on your engines but I can't imagine Suzuki would make it THAT difficult to remove the filter. I'd like to think they're not THAT dumb......