ok.. the main advantage ov LVM is that you can resize it without losing any data.
So resize your partition, say /home.
Create logical volume using that free space, sa call it test.
And install the new distro onto the new test VG.
As suggestion would recommend to backup your boot partition as well as home just in case.
the result will be /boot = common for any number of distros (remark = must have enough space , minimum 500MB or make sure that you dont have old kernel images laying around there., but BE CAREFUL
/PV (your main PV)
/ and etc
On a side note.. How about if you buy an extra hard drive....