I think you need two of the endorsements, unless the FAA has issued a legal interpretation to the contrary (I'm not doing that search, but you can). There's nothing in the regs that I know of that automatically grants complex or high performance endorsements to mil pilots.
61.33(g)(3)(III) grants high alt privileges to military PICs. Presumably you have some sort of records that indicate or imply that you completed a military PIC check? Even if you don't have the original flight logs, something like a manpower code in your personnel records showing AC commander or flight lead, or qualification in a single-pilot AC would suffice IMO.
Also, again as far as I know, possession of a type rating does not waive the requirement for those endorsements, as not all type rated airplanes are necessarily complex. Normally you'd get the training and the endorsement, if needed, when you did the type. So I don't think you can fly a king air either.
However...how long ago did you do your military training? 61.33(e)(2) grandfathers the requirement for a complex endorsement if you logged time in a complex airplane before 8/4/1997. The high performance has the same exemption.