From my understanding, the route-map option at the end of the OSPF 'default-information originate' command is only used for conditional advertisement where a default route will only be advertised when certain other routes are present in the routing table.
So in your example, when BGP is down and the BGP default is withdrawn, a default route still exists in the routing table via the backup so the route-map is still matched and OSPF advertises the default to its neighbors.
A workaround is to use conditional route advertisement with object tracking. Here we can setup a IP SLA monitor to ping your BGP neighbor and if successful install a dummy route in the routing table, this dummy route is then matched in the route-map and allow OSPF to advertise the default. If the BGP neighbor is down, the IP SLA fails and the dummy route is withdrawn resulting is OSPF from withdrawing its default route.
I think the matching on the tag should work fine although Will seems to be suggesting you can't do a conditional advertisement for the default route when the route you are checking for is the default route so as you say it would need testing.
In terms of using match source-protocol i found this document which states that it just does not work for OSPF conditional advertisement so it may just be you were unlucky in choosing that specific option -
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