How to boost performance of virgin queries in MS SQL Server?
Your question can be basically rephrased as 'How does the query memory grant work?'. A good read on the subject is Understanding SQL server memory grant. Before a query is launched into execution it may require a memory grant for sorts and hashes and other memory hungry operations. This memory grant is an estimate. Based on current system state (number of requests running and pending, memory available etc) the system grants the query a memory grant up to the required amount. Once the memory is granted, the query starts execution (it may have to wait in the dreaded 'resource semaphore' queue before it gets the grant). At execution it memory grant is guaranteed by the system. This amount of memory can be shared with data pages (since they can always flush to disk) but never with other memory usage (ie. it cannot be subject 'steal'). So when the query starts asking for committed memory from its grant, the engine will deploy what you call 'strategy #1': data pages may be evicted (flushed if dirty) in order to give the query the memory it was promised. Now if the estimate was correct and the grant was 100% of the requested memory, the query should not 'spill'. But if the estimate was incorrect (boils down to cardinality estimates, therefore is subject to stale stats) or if the query did not got the entire grant it had asked for, the query will 'spill'. This is when tempdb comes into picture and performance usually tanks. 

The only knob you have at your disposal that controls something in this process is the Resource Governor.  Since the RG can be used to specify a MIN setting for a pool, it can be used to reserve memory for a certain workload so that it actually gets the memory grant it requests. Of course, after you did the proper investigation that shows that reduced memory grants are the culprit, and of course after the impact on other workloads was evaluated. And tested, of course.

Now lets go back to your original question. If your investigation is correct (a very big if) I would like to point out two problems:


you run in production queries that require memory grants for a web site. This is a big no-no. Memory grants are indicative of analytical queries which have no place in serving HTTP requests.
your queries are probably not event getting the memory grant they request. Again, even more of a no-no for a latency critical workload as web sites are.


So what that tells me is that you have a fundamental design and architectural problem. Web sites are latency driven and should create an OLTP like workload, with no memory grants and with no memory pressure on queries. Not to mention no spills. Analytical queries should be run in offline jobs and store the pre-processed results for quick availability when HTTP requests desire them.