The purine problem is solved by allopurinol. Maybe a small dose increase could reassure you but based on your latest test result, it’s not strictly necessary.
Protein deficency on the other hand… that’s not going to be solved by any drug. And vegans are at risk of protein deficiency (especially lysine). The solution isn’t eating more protein but more plants containing a better protein mix.
So it seems to me your priority should be clear: you should eat soy, beans and so forth. Peanuts and wheat do not contain as much lysine.
About “high purine plant Diet”, we can go over the numbers together if you want but the bottom line is that there seem to be very few plants which have a very high amount of purines. So one plant-based diet can certainly have more purines than another plant-based diet but it’s nothing like the amount of purines you could be getting from animal flesh (or yeast). What matters is the numbers and not relative judgements like “high” or “low”.
Yes, dairy has less purines and a better protein mix than (most) plants but if you pick the right plants, the difference isn’t such a big deal.
We can also go over the protein numbers together if you want but I think you’ll get basically the same information from pretty much any mainstream dietary advice for vegans.