Well, the solution turned out to be as pathetic as it was profound.
The Upgrade Guide (& SUM) recommended a specific target release for MaxDB (with a warning that using any higher a release - e.g. 7.9.8.18/19 might lead to an unrecoverable error during the upgrade - but it turned out that that target release couldn't handle DB stats that hadn't been updated properly.
Our previous, now defunct, SysAdmin didn't plan any regular optimizer stats updates for PRD (he did for DEV strangely enough).
So 7.9.8.12 (latest pre- *.18 install set presented to me on SAPnet) ended up "loosing" all kinds of File Directory Pointers in the Database, causing it to resort to very costly full table scans in turn.
The solution was to download the latest MaxDB Patch set, run a DB structure check and then update all optimizer stats in the DB.
Now it all works like clockwork again.
While I can understand that SAP warns against using 7.9.8.18/19 for the upgrade, I don't understand why they didn't offer 7.9.8.25 among the install sets.
At least on our account, that MaxDB version was only available from the (different) Patch Set location.
And yes, I know "you should always use the latest patch set <...>", but to be honest I normally install Oracle DBs, where using OPatch is just second nature.
I never figured that a download set still officially available from SAPnet could be so broken as to almost wreak our entire system.