Tying down or bending cherry trees

Tying down tree limbs doesn't really restrict growth. In fruit trees, it's used to direct more hormones to fruit spurs to the tied branches for heavier cropping. I do this more with apple trees than cherries.

Yes, it's relevant. This is what OneGreenWorld.com says about it:

Semi-dwarf Colt rootstock produces trees about 80% of standard size. Colt is adapted to most soils and forms a well-branched tree. Sweet Cherries on Colt rootstock can grow 12-15 ft. in height. Compact Stella, Hungarian and Pie Cherries will be smaller.

RootstockDescription:Considered a semi-dwarf rootstock, Colt produces trees about 80% of standard size. Colt is adapted to most soils and is hardy, vigorous, productive, and forms a well-branched tree. Sweet Cherries on Colt rootstock can grow to 12-15 ft. in height. Compact Stella, Hungarian and Pie Cherries will be smaller.

Size at Maturity:8-15 ft. in height depending on variety

Basically, on colt rootstock you're getting 3/4 of a standard tree. If you need a small tree, a dwarf tree would probably be a better choice. Is there any chance you could exchange it? Swap with or gift it to someone?
Otherwise, you'll need to do a lot of regular pruning to keep it small, and one of the laws of tree pruning is no more than 20% off a tree in any one year, or the tree suffers too much and will likely develop diseases or pest infestation in time. The leader branch would have to be trimmed short first, then some taken off side branches.

Oo - that looks wonderful, as does the rest of your allotment! Most impressive. (She says, hurrying off to do some drastic allotment-tidying....)