I understand why you don't want to use straps, but I believe that's not necessarily always the right thing to do. You should certainly try to improve your grip strength (there are articles on here that can give you some ideas), but I do think you can use a strap for very heavy deadlifts.
After all, by playing to your "weakness", you restrict your back and posterior chain from growing - given all the hard work that comes with a deadlift, you might as well go the whole-hog in my view.
After a workout, you can do some ancillery work on your grip to help it catch up with your back/glutes etc.
I resist using straps and work really hard to "get a grip", but I also use straps when I think it's warranted - for me, that's with very heavy deadlifts (3-4 x 1RM).