Nothing on your list should be a problem to your other plants. I would be more concerned with proper spacing, water and light requirements.

Lemon balm spreads by seed quite readily. It is a valuable herb for tea, but could easily take over the whole patch eventually unless you plant it downwind.

The other mints should be kept as separate as possible to minimize cross pollenation, but most mints only come back true from cuttings rather than seed anyway. In my zone 5 experience, chocolate mint needs a bit of coddling to do well; it would probably not be able to stand up to the more vigorous mint varieties.

Thyme, of course, needs protection from the larger herbs or it will be shaded out. In my area, it overwinters only with sharp drainage (eg in a pot) but the soil here is heavy clay.

Basil and parsley are not perennials, so you could position them in spots that your perennial herbs would gradually fill. Parsley will overwinter and reseed if you let it, which is advisable since it also is host to a butterfly (swallowtail, I think).

The Greek Oregano needs to be kept in check as it loves to spread.

The sweet mint spreads like wildfire, too- so keep a close eye on it. I had only one brush of it last year and it crawled maybe a few inches here and there...mostly stayed in one corner, but through the winter it somehow spread all the way across our raised bed (which contained the mint, strawberry plants -approx 6 new ones-, and 4 tomato plant) and this year it's already shooting up and out more. I'm cutting anything that crawls under and out of the bed, but for the most part I'm leaving it be and just keeping it off the strawberries.