Dealing with spectral leakage between two frequency bins
Yes, concatenating the data will greatly reduce the spectral leakage problem.  There will still be spectral leakage of course, but there will be more bins in between your signals-of-interest, so they won't leak as much into each other.

And yes, windowing should help too.  You are already using a "rectangular" window.  I would suggest trying other windows such as Hamming.