Changing rims from 29 inch to 27.5 inch, V-brake problem

The best solution is to use a frame that is designed for 27.5" wheels. For other problems related to wheel size change, see Do 27.5" wheels fit a 29" mtb?. When riding bike you touch the handlebars, saddle and pedals. If the frame is too large, smaller wheels don't help

If you really have to use this exact frame and either have cash to throw around or live somewhere where labour is cheap, it might be possible to add a second set of brake mounts (but find someone who understands welding and heat treatment to do this, especially if the frame is aluminum).

To figure out whether it's possible, you do the rim radius math and see whether it's possible given the amount of slot you have to play with in on your current brakes, or on any available brake.

So, (622-584)/2. You'll be running a rim with 19mm smaller radius. In the usual case scenario of a common v-brake in the middle-ish of the slot, you won't have the adjustment range you need. V-brakes don't differ much in their slot length or their slot position relative to the stud mount, and those numbers aren't given by manufacturers either. There are a few weirdo exceptions on the market that are capable of allowing this kind of conversion when other brakes can't, such as the Paul v-brakes. Going that route you'll be basically inventing your own mechanical advantage ratio; in this direction it will cause the brakes to need closer pad clearances and they'll feel squishy and bottom against the bar easier.

This sort of conversion will put the pedals the same distance closer to the ground, given the same width tire. Pedal strike will become a problem in some cases, but there are also bikes in the world with over-generous BB height to begin with, or more than needed for their application, so you'll need to determine for yourself whether it will be an issue. Don't ignore it though, because it can be dangerous if it's too extreme.

Very few 29er bike models have ever been made without disc brake mounts, and you're buying new wheels anyway if you do this, so just making it a disc bike is likely something to look at.