Hi Daniel,
So sorry to hear of the trouble you are having! My guess is that your issue may be complex enough to require a professional audit, but I will take a stab here and pointing out a few things and asking a few questions. Let me number these points, as they are sort of all over the map.
1. Normally, when you change the business name in the Google Places for Business dashboard, you will be required to re-verify the listing. Were you prompted to do so? Did you receive a postcard and re-verify? Where are you at in this process?
2. If you had a spammy business name on your Google+ Local page, did you also build citations this way? A ranking drop could certainly result from the new, correct business name not matching other third party listings of your business with the old spammy name. This is important and worth checking! If you find your street address and phone number listed anywhere in conjunction with the spammy name, or with any variant of the business name other than what you've provided in your Google Places for Business dashboard, then you may be dealing with the fallout of citation inconsistency and would need to do a citation cleanup campaign.
3. Second issue - I have seen a number of reports of 404 error pages like the one you are seeing coming into the Google And Your Business Help Forum. Check this search out and see if you see your experience/issue reflected there:
http://productforums.google.com/forum/#!searchin/business/404|sort:date
4. Next - is this also your business?
http://www.bringyourownlaptop.co.nz/
Could you be having an issue with duplicate content between the two websites? Always important to check on that.
5. Is your physical location at Level 2, 80 Mount Street, Sydney, NSW, 2026 a real physical office wherein you make face-to-face contact with your clients? Is the office shared by any other business? How long have you occupied this address? That's 3 questions to consider, I know, but important ones.
6. Since I can't look at the +Local page, unfortunately, I cannot diagnose if there could have been problems with it. You've been admirably honest about saying it was spammy, so that leaves me wondering if there could have been multiple violations of the Google Places Quality Guidelines that could have led to your being de-listed. I'm not saying this is what happened, but it is something to consider. I'd read through them and make a list of points besides the spammy business name that you may have violated. You should also try hard to remember what you edited on the listing.
7. Because the Google+ Local page is 404d, you can't click the 'Report A Problem' link on it, so that's problematic, but you could try this troubleshooter: https://support.google.com/places/#contact=1 You can select the 'my listing no longer appears on Google Maps option' and see if you can get somewhere with that.
8. Likewise, you could report the problem in the Google And Your Business Forum http://productforums.google.com/forum/#!forum/business in hopes of getting feedback from a Top Contributor there. TCs have the ability to escalate an issue like yours to Google staff.
Lots of suggestions. I hope at least some of them give you some ideas of what to begin investigating. Good luck with this!