I did my MEI as my initial with the FSDO and it was not an issue at all.

without your CFI though you are more or less useless to 98% of schools. If you have an in somewhere then Id go for it but typically being just a II or an MEI no one will want someone who can only fly the twin or do Instrument training. Just suck it up, get the CFI and do touch and gos and stalls until you cant take it anymore like the rest of us