Hi ggirlluna,
The only latex that I’m aware of that is 100% synthetic is made by Mountaintop Foam but even their 100% synthetic may contain small amounts of natural latex (particularly in the softer ILD’s).
As you know a type 1 latex allergy is quite rare but it can also be much more serious than other types of latex allergies (see post #2 here about latex allergies) and if I was in your shoes at the very least I would consult with your doctor and I’m not so sure I would take the risk.
Vytex dunlop latex (see post #6 here) has also had the most common latex proteins that can cause allergies removed but once again I would also consult with your doctor before considering this as well.
If you do decide to try either one (again after consulting with your doctor) then I would make sure that you are dealing with a reliable manufacturer or retailer that can confirm that any latex they use in their mattress is one of these two types and blends of latex.
Phoenix