Project functionality is extremely slow

Description

After upgrading to EPiServer CMS 9 (CMS UI 9.3.2, CMS Core 9.3.3) the project system is very slow (to the point that we get request timeouts). A request to the project store, when done in isolation, takes around 28 seconds:

http://localhost:7169/epi/cms/Stores/project-item/?contentLinks=6_4848165&dojo.preventCache=1448874750353

After talking with some of the EPiServer developers, we tried removing items from tblActivityLog. Emptying tblActivityLog seems to help somewhat but the request time sample above is done with only ~300 000 items in tblActivityLog.