I have been thinking about this since you posted and I am not surprised by many of the answers. There is really no consensus on straps vs. No straps.
I go back and forth. Sometimes I use them, sometimes I do not.
I feel that sometimes people avoid them for ego and that is a mistake. If your goal is to build a bigger back, then using the proper tools can help. Another way of looking at this is real world strength and safety. The deadlift transfers to real life situations better than any other exercise. Having a back that can handle more than you can grip is a good situation in the real world. If you cannot grip it, and your grip fails but your back can lift way more - you are unlikely to do serious damage when lifting a couch or something heavy.
Right now I do not use straps though. I feel that over time they have become a little less necessary.
What bothers me about YOUR situation is that you are deadlifting 300 pounds. Not 400 or 500. Frankly, I believe most full grown men, with training should be able to lift that. That is not a knock on your strength, we all have to start somewhere and I am far from the strongest guy on this board.
My questions are - how many sets and reps are you doing? How often are you doing it?
My guess is you are going heavy once per week for multiple sets.
As said above, the deadlift is really hard on your CNS and I've begun to learn that once a week heavy can be far too much.
What I would recommend is to back off for 6 weeks or more. Drop the weight to 225 and shoot for 15 reps. Once you can get 15 reps with 225, go to 335 and go for 15. Once you get that for 15, go to 245, etc.
Only do 2 sets of 15 once per week.
Everyone is against high rep deadlifts, but my guess is the higher reps will be very intense, yet easier on your CNS. And when your grip fails at 15 reps, you will have enough stimulation to cause adaptation.
I did the 15 rep scheme just to see of it was easier in my system and while I was surprised that I couldn't sustain it forever and eventually hit a wall, I've owned gone back to heavier lifting and don't need straps at all. I did 425 x 3 tonight with no straps. Not a record for me but close.
And my back failed before my grip.