I am sorry, I can't offer you a better solution. Unless you want to wait till it gets fixed (potentially severeral years), you better fix it yourself with the available means. If you want to increase the chance that the problem is noticed by Garmin, report it to the Support, but most likely they will just send you here, where it will stay unnoticed by the developers anyway.
6 years after the original post, I still run into a very similar problem today and figured I could share some thoughts and a slightly different workaround.
Firstly, it is also my experience that if your run is just slightly longer than the standard distance, say, 1.05k as the OP mentions, Garmin will just give activity time and you will be better off trimming the 0.05 using the trim feature from connect. If your run was substantially different from the standard distance, say you ran 2k, then Garmin is quite good at picking the best 1k within that run and assign the correct record.
If for some other reason you need to assign a record manually, for example, if you clicked "reject" by mistake or if you have an activity with faulty GPS data that you accepted by mistake and now you want to revert to the previous PB, then you can follow the steps below.
1) Manually assign the run where the PB really happened (possibly over a longer distance) as a PB. Garmin will show the duration of the whole activity as PB and you will be disappointed,
2) Download the run where the PB happened to your computer,
3) Delete the run where the PB happened from Garmin connect. This will clear the PB for that distance.
4) Upload the activity from your computer back to garmin. This forces a recheck
5) Go to your PBs in connect and now accept the new found correct record.