Yes, there are some very long reach calipers that would fit. They're made for 20" wheel and BMX bikes, and for some low end mtn bikes that don't have Cantilever brake bosses (what you removed). The problem is that long reach brakes don't work all that well because the long arms are much more prone to flex than their shorter counterparts.

However, in your situation they're your only option.

Here's an example of that one that might work available in the USA