I would try to go to a 3 foot spacing if you can. Three feet is fairly flexible. Commercial plantings trained to the tall spindle system are usually done on a 3-4 spacing. I think you also need to think about what rootstocks your going to use and how much vigor your scion may have. Bud 9 is probably the best choice unless you have a very sandy droughty soil. If you do G11 would be a better choice.
I also think you should look at this tree spacing calculator. It’s from Michigan. There is also a slightly different version available that is tuned for East Coast conditions supplied by UMass at Amherst. You input a bunch of different values like the rootstock, soil type, how your going to water, etc. The calculator then gives you the recommended tree spacing and row spacing.
http://fruitadvisor.info/tfruit/clements/appletreespacing.htm
For example for average scion vigor, Bud 9 rootstock, loam soil, as needed watering, tall spindle system, with target tree height of 7 feet-
The calculator recommends:
2.6 feet tree spacing
9.1 feet between rows
Having said this you need to follow the tall spindle system. If you don’t and go with a central leader system you will end up with a mess. The trees will grow into each other and create a dense hedge. Also for row spacing think about how your going to mow between rows. Your equipment needs to be able to fit.
Since your space is limited I would do controlled cross pollination. I would pick the parents very carefully. Two really good parents will greatly increase your chance of success. Also try to avoid “me too” apple trees. Everyone is working on an improved Honeycrisp and an improved red fleshed apple. And they’re producing hundreds and thousands of candidates. For the small scale breeder you’re better off having unique goals. A Wickson cross that doesn’t crack in the Midwest. A very productive apple tree with Peardrop flavor. Or maybe a Gold Russet -William’s Pride cross which could give you a highly disease resistant apple with great flavor that could also be used in cider.
Any ways these are some ideas. In the end however, follow your heart that is truly what is important.