Should we wait for tests to TTC again?

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So i am already so fortunate to have son who is 2.5 but I’ve had 2 miscarriages since and in UK they only test after 3 as apparently 2 are really common. I went to see a fertility specialist privately though as I am hypothyroid and worried about that plus any autoimmune conditions that could be linked (as it is autoimmune hypothyroidism).

She says she could test but it would take 6-8 weeks for results which would mean delaying by at least one cycle, which feels unbearable to delay. If we don’t delay the test results could come back after conception theoretically. Also tests all in plus follow up would be over £1000! We have this money but it’s a large chunk of our savings (again, we realise we are very fortunate).

I just really don’t want to miscarry again and at that point, the wait on NHS would apparently be 12 weeks for results plus NHS doesn’t test everything apparently. But to miscarry again would be awful and months delay too. I just don’t have faith my body is ok and won’t miscarry again.

Has anyone had recurrent miscarriage tests and what did they include? Any thoughts on what to do or anyone else had similar situation happen?