Are your arms fully extended in the movement? If you bend your arms, you might be straining your biceps which can cause elbow pain like you're describing. Be careful with this. When you get up to much heavier weights, you run the risk of a bicep tear. Flex your triceps when initiating the movement.

If you won't use mixed grip, use hook grip. If you can't stand hook grip, you can use double overhand like you're currently doing till your grip fails, after which you can use straps. You can do supplementary grip work later on.

Hook grip ain't for everyone. I can't do it too. Mixed grip for me.

I still don't get how you can injure your elbow and forearm from the bar slipping though. But anyhow, yeah, straps are a good. Just make sure your grip gets the training they need as well.

Yup, I agree. Your grip will improve regardless with straps or not. Pete Rubish is an example of a powerlifter who trains like this. However, your grip will have play catch up when you use straps exclusively. Doing grip work separately is an excellent strategy as well. I know some people who squeeze their grippers during work hours to help pass the time. Some people do extra grip work after their sessions, it usually doesn't take more than 10 minutes.

For me personally, I really don't like doing extra work. In my sport, straps aren't allowed, so I've been training exclusively without straps ever since I started, except of really high rep sets. As a result I've never had to train my grip at all, never needed to do extra grip work. It also allows me to gauge what I can actually hold on to come meet day. If I can't hold on to a certain weight, then I know I have no business in attempting it.

Only recently my grip gave me some issue when I pulled my new 1RM of 171kg. Below that my grip stays solid and I can stay locked out at the top for a few seconds if I wanted to.

Double overhand or mixed grip? Double overhand, my max is 130kg I think. Tried 140kg before but it slipped right at the knee.

I can testify the efficacy of heavy Kroc Rows. Amazing exercise for grip, core and back.