Is this batch of sauerkraut salvageable

In general, slimy brine is indicative of a fermentation problem. Your brine might be too weak (what concentration did you use?), it may be too warm, your brine might not cover the vegetables, there might be some air bubbles trapped in your ferment.

This article suggests that in the early days of sauerkraut fermentation, the concentration of slime forming bacteria - Leuconostoc - is relatively high and towards the end of fermentation it's too small to measure. It doesn't say anything about slimy brine, but it's possible that the brine is temporarily slimy in the early days of fermentation and as the acidity increases it dissipates. I've never checked a ferment this early, so I can't comment on it.

Personally, I would let it continue to ferment for a week or two and then see whether the perceived sliminess has dissipated or increased. It's possible that it's too early to tell. Slimy vegetables, without a doubt, should be discarded.

References

• http://www.culturesforhealth.com/fermented-vegetables-troubleshooting-guide

In my experience a month is a bit long (although of course this depends on the size of the batch, etc) for active fermentation - however I don't think that's the problem. In fact, I don't think there is a problem. Since Sauerkraut is a 'wild' food, there are some variables that you can't (and shouldn't) control.

The most likely (85% sure without knowing other factors) situation is that your kraut has picked up an uncommon variety of wild yeast and that yeast is doing its thing and putting-off this sugary/sweet smell as a byproduct of its processes.

Are you doing anything different with this batch that you've not done in the past? Fermenting it in a different part of your house, maybe? Is the temperature unseasonably warm/cold? Regardless I think you'll be safe and come out with good kraut (which doesn't seem to be your concern) - but if you come out with REALLY good kraut, maybe you'll want to try to duplicate your experience :)