Some questions because i've dealt with something like this before with AP roaming but it was related to a swirtch stack which might not be the case here.
If it is a switch stack, are the AP's connected to different switches or the same?
FWIW - The decision to switch AP's is both client and AP side normally. To my knowledge Meraki currently doesn't allow a manual configuration to set a signal threshold on when a AP drops s client due to signal, the amount is unknown to me. On the flip side - you can sometime configure that information on the client.
The general solution right now is add another AP or potentially reduce the transmit power of one AP and play around with it are my suggestions.