Install a flush tension head solid rivet in the flush shear head countersink... then carefully mill-off the excess-head-height flush. May specify a reduced bucked-tail to match the reduced head after milling.
Install a protruding tension head rivet with the manufactured head on the non-flush side... and then drive the tail into the countersink. Mill-off the excess bucked-tail height flush-to-slightly high.
CAUTION: These two options may require the shop to develop techniques to accomplish work successfully [shear testing may be required].
Install 718 Inconel flush shear head Hi-Lok pins and A286 collars... or may install A286 or Inconel [silver-plated] hex/2X-hex nuts to a relatively low [shear-rated] torque.
For smaller diameters, flush shear head Inconel blind rivets are available [1200F rated].
NOTE: there are Huck and JO-Bolt style flush shear-head A286 blind-bolts [commercial P/Ns] available... but I am not sure of the max temperature rating.
CAUTION: all rivets or pin fasteners should be unplated... whereas all mating nuts/collars should have silver-plating.
zhangtl: BACR15CE*M rivets are Monel, not Inconel.
wktaylor: I like your thinking. Do you know of a spec. for the small diameter blind rivets that you mention? (The diameters I'm after are 0.125" and 0.156")
What installation method are you able to use for a fastener with temperature above 1200f
one of your requirements was a reduced CC head, what is your parent material thickness
are threaded and or blind fasteners an option?
The (2) rivets specified have MS20426 style/size heads... but are 1/64" oversize Dia... resulting in shallower depth heads than nominal Dia MS20426. The oversize for both the NAS1097 and MS20426 style [blind-rivets] are the rivets noted. Check specs for ACTUAL head depth.
NOTE: IF You can tolerate it, specify a countersink that is 0.005--0.015" SHALLOWER than the nominal 1/64" head depth... and "allow heads to ride above flush. Way I would say this is as follows [example for 5/32-OS rivet]:
"Countersink 100-Deg X 0.037+/-0.005-deep (rivet heads may ride above flush up-to 0.015)"
... or what ever Your needs are.
CAUTION: You indicated that the top-sheet is 0.050 and the stack depth is 0.082 implying a 0.032 backside-sheet. The 0.032 is awfully thin for driving ANY 5/32" solid or blind rivet: the hole may buckle/distort when the rivet is driven or set. In this case suggest considering a 718 Inconel FSH Pin & Shear Collar MF Hi-Lok combo... or spot/seam-welds.