I can't imagine any reason you would have 3-4k seperate module instances in a single site, even in a huge community like myspace this isn't done. But, I don't know the requirements so I may be off base. What I am really getting at here is I need to understand how you plan to use it. It's one thing to have a single module instance w/ 2-4k forums (which would be impossible to use), but that many module instances baffles me. I also need to know if you plan on having these in a single portal or in a single install w/ many portals.
To be very blunt about this, if you need this many forums I don't think there is a single forum module available for DNN (I don't even think php or other .net solutions would do this well) that will meet this requirement. The max hits I have heard of using DNN is around 500k/hour and this is on a farm. If you had 10 people each on the 5k forums, you would easily top this 500k page hits/hour.
All those numbers aside, the uphill battle you will have with any solution is the amount of data. Lets just talk about 3k forums. This means there will be 3k forums, each having at least 10 threads within the first week. Let's say each thread consists of 3 posts, you are at almost 100k records there in the posts table. Even though you are isolating this to about 30 records per forum instance, it still has to sort through those 100k. I've worked w/ larger data applications where single tables have gigabytes of data stored and unless you are on a really beefy data server this is going to be slow.
All the theory behind us now, I don't think this module would be able to do this. I am in the middle of refactoring it for performance and for better usage in a multi-portal environment and depending on your hardware setup and how you are going to implement this (single module, multi-portal, etc) I know it would work after the refactoring but I have a feeling it will be slow. (I feel any other forum solution would be like this too and hardware is definately the limit here).