The general rule is the diameter of your anemone should be 2.5x the length of the clownfish as a minimum with 3.5x being better. I would never recommend less than 3.5x. That said, your anemone should be about 10" in diameter to host a 4" clown. It doesn't take long for a healthy BTA to reach 10" but it won't take much longer than that to outgrow your tank either. Although I am of the (controversial) opinion that anemones do not belong in full reefs, I'm very comfortable saying that no host anemone should be in a nano tank. They all grow too big.
Now putting that aside, have you figured out what killed your other anemones? That would probably be the first thing I'd want to figure out and fix. BTAs are the hardiest host anemones - well maybe LTAs - and can usually tolerate a lot.
With regular water changes your 75g is a fine size. Don't let the lack of skimmer scare you. Anemones need clean water but I assure you a healthy BTA will survive long periods of "less-than-pristine" water quality. If the skimmer is the only thing stopping you, the anemone should be fine in there until you do get one.