Is there a specific order for -bo- and -ge-?
No, both "bogepatroj" and "gebopatroj" are allowed by the PIV (a Esperanto monolingual dictionary).
I typed "gebopatrojn" and it was marked wrong, with the note "The normal expression is 'bogepatroj'." So...is it technically correct, but so uncommon to say, that it would raise some eyebrows...?
You wouldn't raise any eyebrow. I don't think I've ever talked about "parents-in-law" in Esperanto, but I think I would prefer bogepatroj, but there is no reason for gebopatroj to be wrong (the order of prefixes doesn't change the meaning here).
Tio estas vera por mi.