The first thing I tried was pressing the spacebar down somewhat with a few strips of sellotape, so that only a small push would be required to get the bar to its activation point. This did work - for a single keypress: after pressing the spacebar it would hang.
The second thing I tried did, on the whole, work as intended - and I am using the trick right now. It occurred to me that I could try to counteract the upward pressure exerted by the spring underneath the space bar by adding weight to the bar itself. So I sellotaped two magnets I had handy to the bar and, voilà, a much lighter typing experience:

Obviously, there are a few disadvantages. This solution is not very attractive aesthetically (but then I rarely look at the keyboard itself). Also, due to their shape the magnets do occasionally get in the way a bit. And, finally - as well as most importantly - the magnets are a tad too heavy. Occasionally, the space bar hangs after I've pressed it. Each magnet weighs 20 grams; 15-17.5 grams (with a total weight of 30 to 35 grams) would likely be better for the purpose I am now using these for.
If I can find something with a better size and shape (as well as weight) I will try taping that to the spacebar, but for the time being I think these magnets are going to stay.