I agree with digit. Some way needs to be done to find out how to best regrow this strangeling, as Luther Burbank himself might have called it.
I'll just think out loud a bit here some too. You live down south which should mean a good long season.
I'm not sure if Potatoes, strangelings or regulars, need to have their tubers go dormant for a certain period before resprouting or not.
But if the tuber needs no dormancy you should have a good 90 days to grow it out. I'm sure digit knows what he's saying, but to me, 60 days seems a bit minimal for potatoes. 60 days'd get you baby potatoes though. Maybe that's all that's needed.
Either way, a good dusting of sulphur, or at least some good wood ash, on the strangeling would protect it from rot.
More outloud thinking. If it really is a cross it'll be either POLYPLOID or TETRAPLOID, and will have an amazing set of GENES, in combinations rarely if ever seen. This kind of GENUS CROSS rarely happens in the SOLANACEAE family. In the BRASSICACEAE family however, Genus crosses happen quite a lot.
It may be good to contact CORNELL UNIVERSITY about this. UC DAVIS, and other agricultural schools would want to study the genetic makeup of this. It could become something important. They will want to know exactly what variety of potato was a parent, and what variety of Tomato.
Potatoes do have some TETRAPLOID varieties. I don't think there are any tetraploid Tomato varieties.
Some of those new true purple varieties of tomato are the result of new geneflow from a different species of wild tomato. There has been geneflow from wild tomatoes to domesticated tomatoes all along, and once in awhile a different wild species such as yellow currant tomato is crossed in.
What I'm getting at with this is that with the different species of tomato, (actually subspecies, but convention calls them species), there may have been an introduction of a chromosome that breaks successfully, or has a satellite portion that could behave as a separate chropmosome. That would be the sort of mechanism that could possibly allow the WIDE CROSS.
I have been readiung some recent scientific american magazines. There is now the ability to GENOME SEQUENCE an entire organism on a machine that costs a cool one thousand bucks. This machine is the size of a home computer printer. This means that universities all over the place will probably get one.
Whatever you do, save a piece of it. The above ground plant. Save a piece of it. Preserve its DNA.