Hotplug li-ion in parallel for a custom battery pack
The best scheme would be to not actually be trying to put the battery packs in direct parallel for the reasons that you have cited. A better approach would be to design it so that only one battery would drive the computer through a MOSFET switch. A second battery would be switched in automatically through a second MOSFET switch. A control circuit would manage which battery pack switch was active and auto switch to the alternate battery when the the current battery is depleted. The main point that only one battery MOSFET is ON at a time.

A sensor in the control circuit would provide the indication when the battery became depleted and a switch over was necessary. An LED would be placed by each of the battery packs with it being turned on to alert the user that the battery back that needs swapping out.

You would equip the front end power connection to the computer with some capacitors sized to keep the computer powered through the short time that the control circuit switches off one MOSFET and turns on the other MOSFET.