Did Black Miss A Draw?

HAD a 64-move rook-and-pawn ending in round three of the Bad Wiessee Senioren-Cup today … and it seems my opponent missed instructive draws on consecutive moves.

The rook-and-pawn ending began with White to make his 28th move in Spanton (1880) - Elof Cordts (1701)

White is about to go a pawn up, leaving Black with four isolated pawns, including two that are doubled.
I certainly thought I was winning, and the analysis engine Stockfish10 agrees. But another very strong engine, Komodo9, 'merely' gives White plus-over-equals - after all, it is a rook-and-pawn ending!
The critical position came 50 moves later:

White has just played 78.Kf4-f5

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78...Ra6
I thought Black had to play 78...Kg7. After 79.Rd7+ Kh6, the first point is that White cannot play 80.Kxf6 as Black draws with 80...Ra4 81.Kf5 Rf4+! (81...Rxg4! also draws). If instead of 81.Kf5, White tries 81.g5+, then 81...Kxh5 is a tablebase draw.
Since 80.Kxf6 does not work, White is more-or-less obliged to try 80.Rf7. Then comes 80...Ra5+ 81.Kf4 (81.Kxf6 is met by 81...Ra4 with a draw as before) Ra4+ 82.Kg3 Ra3+ 83.Kh4 Rf3 84.Rb7 (84.Rxf6+? Rxf6 85.g5+ Kg7 is a trivial draw) Rf1, and there does not seem to be any way for White to make progress.
One line given by the engines after 84...Rf1 goes 85.Rb4 Rh1+ 86.Kg3 f5! 87.Kg2 (87.gxf5 is the notorious drawn ending of f+h pawns) Ra1, and the best White can get is again the drawn f+h pawn-ending.
Where possible I have confirmed the engines' conclusions with the Nalimov endgame tablebase, so it does seem Black missed a draw. It is perhaps needless to say that neither player was aware of virtually any of this during the game.
Going back to the second diagram and the game continuation of 78...Ra6, there followed …
79.Re4 Kg7?
It seems Black still had a draw with 79...Ra1! (or 79...Ra2! or 79...Ra3!). Here the point is that, after 79...Ra1!, White has nothing better than 80.Kxf6, but then Black has a tablebase draw with 80...Rf1+ as the White king has to let its counterpart into g5, after which the draw is relatively simple. No wonder Tartakower (or was it Tarrasch?) quipped that all rook endings are drawn.
After Black's second missed drawing chance, the game finished:
80.Re7 Kf8 81.Re6 Ra4 82.Rxf6+ Kg7 83.h6+ Kh7 84.Rf7+ Kh8
Black meets a swifter end after 84...Kxh6? 85.g5+ Kh5 86.Rh7#
85.g5 Ra8 86.Re7 Kg8 87.g6 Ra5+ 88.Kf6 Ra6+ 89.Re6 Ra8 90.Rd6 Rb8 91.Ke7 1-0