Wow congrats! youve made some serious progress!
First off I would recommend a little bit more research on GH, there are plenty of threads here and a lot of studies you can reference. Only reason I say this is because GH may not be what you expect. a lot of friends I have had use gh get great results but the initial use was not what they expected in terms of it's side effects. In regards to T4, yes you can run T4 alongside it but thats entirely dependent on your bloodwork and side effects. GH can reduce secretion of T4 but most of the studies were done in vivo, in vitro, on animals, and in GH deficient adults.
Keep in mind those with a hormonal deficiency can have very different results with a specific hormonal treatment than those who do not have a deficiency. There are several studies (you can google it) that highlight the correlation of GH treatment to T3 and T4 secretion.
My recommendation: get some T4 just in case. do a blood panel for metabolism and GH, note your baseline and if you see any decrease in metabolic panel you can consider using t4 if you notice large decrease in your t3/t4 levels and if you notice lethargy.
If you can find that thread, please bump it to share. Personally I have never ran gh and T4 together but I would love to read more on a protocol for it.