Welcome to the boards.
I will say having a 700H puts you very much on the new side of this group, 16 years newer than my 450E. Hopefully someone familiar with them will chime in with some help on your problem. Have you called your JD dealer and asked if they might have encounter this before? There might be a common issue they have seen with these.
Your machine is hydrostatic drive, has a computer, and at least some electronic controls, doesn't it? Does it show or allow you to bring up fault codes? My first thought is to check electrical connectors. A lose or dirty connector can do funny things. Also look for a pedal, or linkage, not fully moving back or a stuck switch. Do you have the technical manual set for it? TM1858 the operation and test manual should have wiring diagrams and testing/diagnosis info. TM 1859 the repair manual gives the nuts-and-bolts info of making the repairs. Below is a link to the TM1858 manual on the JD Construction and Forestry bookstore. As you can see on the lower part of the cover page preview, along with the TM1859 repair manual there are several component manuals listed as well, some of those may or may not be needed. TM1858 should have the info to get you started on diagnosing the problem. When you open that page, you can check the other manuals by typing the publication number in the center box and hitting the search. The Operator's manual (TM201705) is free to view or download there as well, if you don't have a copy. I took a quick look at the operator's manual, and it looks like there could be some info in section four that might help you.
TM1858
If you don't have it here is a link to the 700H online parts catalog yu can use and print info from.
700H parts Catalog
Sorry, I know this isn't much help. When you find problem, it would be great if you would post the cause and fix so we can start building some info on newer machines. Good luck.
Jim