The main reasons for getting frequent blood tests early on are:
-the allopurinol starting dose is low so as to minimize the damage in case you don’t tolerate it well but in case your system does handle it well, you’ll want to increase that dose quicker than every 6 weeks in order to minimize the length and severity of the numerous gout attacks people often get after starting allopurinol
-if on the other hand it turns out you do not tolerate allopurinol well, you will want to try an alternative before the side effects turn your system into a mess
It often doesn’t take many weeks for clear clues to show in blood tests.
As to spinach in the purine list you found, it sounds about right. Spinach is only high in purines relative to the amount of protein and energy it contains.
Such lists shouldn’t be used a list of “good” or “bad” foods but as a guide to how much of any food you can eat before it might become a problem in terms of purines. And the amount of purine in the most nutritive foods shouldn’t be compared without adjustment to the amount in the least nutritive foods. Else there would be a way to make anything into a low-purine food: simply add water.
That said, there are issues with the purine list you linked to. There are several types of purines which have a different effect on the body. Most plants do not have the worst purine type. For instance your list might lead you to conclude that soy beans are slightly worse than chicken in terms of purines while they are actually much better.
Unfortunately, I don’t know any comprehensive list of foods which breaks down the purines by type.