Remember that you can choose any date for your super priority appointment you like and that you only have to submit the online application by May 8th.
So, if you wanted to buy some time, you could apply online at the end of April or early May, but then choose a super priority appointment date a few weeks later in late May. That way, your visa would be issued in late May 2020 and would expire in late November 2022, which would give you 1.5 months to apply for ILR (11th October to late November).
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