I have really small hands, and short fingers. On a piano I can reach an octave and a little more, but my octave is generally very sloppy. A lot of songs require some crazy octaves like Liszt's Liebestraum. The part where the melody is played by octaves and leads up to the cadenza (I think that's what it's called). Also, like Revolutionary, the main melody is octave. I generally just lower my hand a little bit and point my hand upward then play with the edge of my fingers. It's doable but inconvenient. I can generally play chords that span an octave, but can't play the octave well...so I doubt there's anyway around it unless I get surgery on my hands or something.
It sounds like my fingers are a similar length to yours. I found that the important part of reaching the octaves confidently was flexibility rather than length. Your thumb and pinky finger (or even your ring finger) can bend back further than you might think. Never force it though. As with most aspects of playing, I'm afraid it just takes time and practice to stretch comfortably.
Try playing octave scales regularly to get your hands used to it. Also try playing scales using 7th and 9th intervals (instead of octaves). It doesn't sound very tuneful, but it can help build up your strength and accuracy. From there, try running up and down scales playing full octave chords (i.e. play the major chord for whatever your root note is... e.g. C major, D major, E major, and so on). If you're feeling adventurous, try playing 1st or 2nd inversions instead so you get used to your hand being at slightly different angles.
Always warm up a little with scales etc. before you do the stretching though, and go slowly at first. You need accuracy before building up speed. Also, try to keep your hand relaxed at all times so you can stretch safely. Given enough time, you might be surprised by how far your fingers will reach.
There are advantages to small hands as far as quickness in passages requiring tight, compact scale work. Some people with big fingers stumble over their length in these situations, others have fingers too large to slide between the black notes which is another disadvantage.
I'd say longish fingers that aren't too fat giving you a reach of a tenth is ball parking "ideal" and short fat fingers without reaching an octave or being able to slide between black notes is the least ideal.
Nevertheless, diligent people create workarounds and make great music regardless of their natural build. Milan kundera said the concept of idyll is the worst thing to ever befall the human race because we feel forever inept compared to the perceived possibility of perfection we can't reach. I tend to agree, best just presume you can become strong following known practices, a bit of your own gut instincts and working hard to make it happen.
Oh and least important of all is to have fun. Joking
Of course, with problems of matching instrument and player anatomy there is always the last resort of changing the instrument to something comparable but better-suited.
With the piano, the standard concert instrument is the grand piano, and the grand piano very much has a standardized key width. So unless you are playing at a level where you are expected to bring your own instrument, the piano is really not accommodating different player anatomies.
While upright pianos are not really used in concert, the situation may be different for cembali and some other keyboard instruments like celesta.
Smaller key sizes but a significantly different playing style and repertoire differing from the percussive character of the piano, are offered by organs, harmoniums, accordions, particularly chromatic button accordions where even small hands can easily span two octaves. While few people are expected to bring their own organ to a concert, the other instruments can reasonably be bought and/or at least transported personally.
At any rate, it might be worthwhile seeing whether acquiring skills on a more hand-friendly instrument variant can offer new perspectives. Whether to make a full switch at some point of time may be a different question.
I can confirm the stretching aspect. The distance between tip of pinky and tip of thumb on my left hand is noticeably longer than on my right hand. This is due to 8-10 years of typical left hand positions of playing large intervals. Now I find myself attempting to play a major 10th that involves white and black keys (example: E major, 5 on E, 2 on B, 1 on G#) <- difficult....
Note: I am 6'2 and have bigger than average hands.