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......we know of several units that operated the Bf.109H. ...
You might be thinking of the Bf 109T which was developed for the 'Graf Zeppelin' .
As far as I know, there were three Bf109H aircraft built:
V1: WNr 16281/SP+EB
V54 : WNr 15708/PV+JB
V55 : WNr 15709/PV+JC
From the looks of the airframe (including bulges on the cowling) I would say it was a modified G series
One did see service with 5.(F)/123 (Recon Group) in Spring of 1944 from April until July.
Here's a couple pics of PV+JB
View attachment 190012
View attachment 190013
"MODEL" of PV+JB?
Accordin to "Warplanes of the Luftwaffe" by Daid Donald, these were the planned versions of the 'H'....
Bf 109H-0 = Pre-production version
Bf 109H-1 with DB601E engine
Bf 109H-2 with Jumo 213E engine
Bf 109H-3 with Jumo 213E engine
Bf 109H-5 wth DB605L engine