Compare the length of your top tube with that of a comparably sized modern frame. I believe UO-8 top tubes are considered longish; mine certainly is, which is also why I can ride a small 54cm frame comfortably.
A handlebar 3-4"/8-10cm below the seat is probably too low, unless you are into serious time trialing. I keep the top of the drops 1.5-2"/4-5cm below the top of my saddle on my road bikes, and that is already a very aggressive stance, particularly if I bend my elbows. I, too, am 54 years old.
__________________
"Far and away the best prize that life offers is the chance to work hard at work worth doing." --Theodore Roosevelt
Capo: 1959 Modell Campagnolo, S/N 40324; 1960 Sieger (2), S/N 42624, 42597
Carlton: 1962 Franco Suisse, S/N K7911
Peugeot: 1970 UO-8, S/N 0010468
Bianchi: 1982 Campione d'Italia, S/N 1.M9914
Schwinn: 1988 Project KOM-10, S/N F804069