The thing to consider if you go for a triple, is that you might well need to change the rear mech as well as chainset, bb and front mech. Not many vintage rear mechs (since we are in the vintage forum here...) could wrap a triple (with typically 20T difference) and a 14-28 block (14T difference) at the same time.
Imho a 46/36 chainset is a reasonable step to take. From what you said I suspect you are spinning at 90rpm or more at the pedals which a 46/14 should give you around 24mph. If you wish to have a higher top speed depending on number of speed you have you might be able to get a rear block (I am again assuming you have a freewheel not cassette) starting from 13T.
With a 46/36 I think you should be able to get away with not changing your front mech. You will have to move it down the seat tube by about 12mm though. Just make sure you get the right BB that delivers the same chainline you have currently, and shorten the chain by at least two links (one pair).
The other option that might be worth considering if bigger gaps between gears don't bother you, again depending on what speed block you have and rear dropout distance is to consider changing to a wider range block without touching the chainset/bb/front mech. 13-34T freewheels are readily available, e.g., but you will also need to get a new, longer chain and change the rear mech (which is neither difficult nor expensive, assuming you have friction shifts or if indexed Shimano).