Yes taking them out is easy I always use the ribbon thing. I have been putting them in angling the positive side first. Perhaps that is the problem.
That is the correct way.
Especially if the batteries are not over-wrapped on the NEG end.
Just an afterthought as to how you might protect the wrapper in your case.
You may have to use something like a plastic shoehorn to collapse the NEG side so you have room. Put the shoehorn in before pulling or pushing the batteries. The shoehorn would look like those tabs used when shipping a device with batteries in it, but you have to pull them out before use. You can cut a strip from an old plastic credit card that should be stiff and thin enough ( I use CC stock for a lot of different fixes). Use your thumb on the battery to slide the NEG end back on the spring so you can get some room to insert the plastic on the POS end to take them out. Just hold the plastic there when inserting then take out.
Look at how the negative end is a rounded button.
The POS end needs to be the same, and protrude less (dremel?).
If the dorks that designed it actually flipped the connectors around, it would work without damaging the cells as the POS end would collapse freeing the NEG end and and battery could be rotated out/flipped out from NEG end without hanging up on the wrapper. Sounds like a fix that could be done by someone w/ experience.
Keystone, other sleds and some chargers have the same issue. Below is a pic of a modified Keystone sled.
Note the dotted line. This is where the tang originally lay. It is pictured where it should be.
Original position it would hang up on wrapper.
The ellipsed area is critical. You can see how the tang has room to move past the plastic of the sled - the slot is wide enough to allow the tang to collapse a little without binding (not enough room to insert battery if tang could only move a little). This feature I have found to be unique to Keystone.