I recently popped a blood vessel in my palm, while trying to deadlift heavy (for me, 355 lb) on a wobbly platform (I have since fixed the platform). This recurrent bruise makes it hard to deadlift heavy, causing a lot of pain on a max tightness hook grip.
In order to continue deadlifting, I've gotten a pair of straps. However, I'm worried about keeping my grip strength on par with my deadlifting ability. Are there other "sub-max" grip exercises I should consider, to keep training my grip while recovering from this injury?
Experience seems to contradict your statement. After your thumb gets used to being squashed (3-4 deadlift seasions) you can deadlift around the same what you did with straps. Even if you did not used hookgrip ever before. It happen to me and everybody else who i trained with. Your grip gets stronger from overhand grip warmup sets, preses and pullups. Usualy that is enough.
And my experience says the heavy deadlift sets with hook drive grip strength more than anything else you've mentioned. I've pulled 220kg DOH with my previous best being 200kg, and in-between all I did was deadlift heavy sets of 5 with a hook grip. A 20kg jump doesn't seem possible if the DOH warmup sets are the real driver.
Train all your warmups with the hook grip and build it up. Do that for all of your deadlifts, and your cleans as well. Worked fine for me. I'm at the same PR deadlift as you.
Lidocaine will not numb a deep bruise.
This is true for me as well, though I have stubby fingers and I can't just hool grip and go, I have to hook grip while also squeezing the shit out of the bar. So for me hook grip works grip strength as well as my fingers aren't long enough to do hook grip with an otherwise loose grip.