You best solution is to use anything other than a repeater to solve your problem. Even in the very best case a repeater will lose half the throughput it generally loses much more. It will also degrade the machines directly using the main router but how much is hard to say. You are trading coverage for performance.
It likely will work with the belkin since it supports WDS and even though it is not a standard most manufactures have implemented it the same way.
Be aware the repeater you are looking at only support 2.4g. It also does not support mimo ...which is the thing that give you 300m. It is unclear if it supports wide channels or not. So if it only supports 54m you will get at the most 1/2 or the 54m and you never even...