That was quick. I cut up a key stem from a spare key and tried it in the spare barrel. U used a little hot glue to connect it to the space bar. This means that the space bar was getting double the spring force back. I am typing on it just now.
First impressions are that the spring force required is now too strong rather than too weak. Feels like a little too much effort to type on now.
On the positive side, I can tell you that the barrel in standard configuration does virtually no stabilisation. The round section on the space bar moulding has too wide a circumference to contact the empty barrel in a meaningful way. With the extra key stem the space bar becomes more solid with less lateral movement. I am thinking that I will probably keep the key stem but shorten the spring a little.
If you have a spare key that you are not using you might want to try modifying the space bar to take advantage of the spare barrel.