Ran into this problem on Friday afternoon. Very similar - WriteLog waits, then TM Request. I am using Ola's PerformanceStore and the spids associated with a slow query etc. would have a batch_statement or statement, but NONE of these spids have an associated code snippet. There are no waits for then as well. I did see, at the sametime, the following wait_types for other spids, equally affected by the problem:

PREEMPTIVE_OS_CRYPTACQUIRECONTEXT

PREEMPTIVE_OS_CRYPTIMPORTKEY

PREEMPTIVE_OS_CRYPTOPS

PREEMPTIVE_OS_DELETESECURITYCONTEXT

PREEMPTIVE_OS_WAITFORSINGLEOBJECT

I know that CPU went to 100% for a minute or so, so not sure if these are causal or symptomatic of another problem. But I would expect to see CPU-related waits along with TM Request command.