Hi Tim,
In this case using the index table engine is the only way – because there you can select which taxonomies to index, in your case only choosing the post tags will do the trick.
The second issue is a bit more complicated, it might not be possible. Using the default ‘AND’ logic + the index table engine could work in a similar way, but it will always match other fields as well, so not only the post tags, but any other field that is indexed (content, titles etc..)