Anyone thin their tomato clusters? My early girls, for one, have 4-6 tomatoes on each cluster.

No need to thin tomatoes. They will only set what the plant can support.

The plants are some of the biggest/healthiest I've ever seen let alone grown, so the support isn't in question. I meant the question more towards the development and quality of the fruit.

If you have several, experiment. Thin one cluster, leave another alone - and tell us what works best.

Being in the open with sunshine and air breezes hitting them is more important than how many in a cluster.
Healthy soil will do more for larger yield, size and quality than thinning BUT it does work for growing record size fruit so it may give you fewer but larger fruit.
I do remove all leaves up to about sixteen inches to two feet off of the ground and higher when they get larger.
More air circulation reduces disease problems and even though the leaves supply strength to the plant they also take energy for the plant to keep them there so as with trees, less is more, more or less, unless you have to work with Les Nessman.