What do we like for a bigger tomato as a sandwich slicer?

Beefsteak. My old man would pick them off the vine, salt them and eat them.

Love me some Cherokee Purples, they get almost as big as a beefsteak, but the flavor is a whole different experience.

Consider looking for "heirloom" seeds or plants. I just ran an internet search and there are lots of options.

The local farmers always has a couple of growers/sellers who have amazing tasting large tomatoes.

Also the Heirloom tomatoes, those not GMO or hybrids, will come back true to original if you just save the seeds from inside your tomatoes. You can grow the same thing year after year.
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Oregon Star or Black Krim.

I haven't had much luck with so-called heirloom varieties. They grow and produce OK, but seem to be much more subject to insect and disease attacks. So much so that much of the fruit is unpaletable (decayed mushy spots, rust, etc.) Generally, I have found them inferior to common hybrids like Big Boy, Better Boy (which is way less "better" than Big Boy), etc. Also, I'm not hung up on one slice to a sandwich, I have been known to sandwich multiple slices of smaller fruits, call me an infidel if you will, but hey, the smaller fruits usually have more and better flavor, fewer seeds, and less juice.

Trying a Territorial seeds heirloom Genuwine this year. I've had good luck with Territorial seeds. They're a little spendier than your OTC stuff, but they're quality.

I like Rutgers for a slicer. Nice flavor, they do well in the heat and humidity, grow quite a few per plant, and they have a consistent size from first to last.

Very large tomatoes have a hard time in the South, and we have to be pretty picky on variety. Very few varieties set fruit above 80F so that attribute is a higher priority than size. I'm also looking for a consistent size, and don't want my first one to be 16 oz and my last one 3 oz.