Consider this: If you were a student or employer, who would you pay the $$$ for instructing: Someone with 30 hours multi, or someone with many hundreds or even thousands of hour multi? Who do you really think would offer the most to a student to keep them alive once they have their ticket? There's more to a Part 23 certified multi than just the basic engine failure drills.
You need to get a job with a mob somewhere that will lead to multi flying. If that means sticking with your present job until you meet 135 mins then do it! It's for a limited time, after all. That opens a lot of doors - there are rather more 135 multi operators than S/E only. The FARs don't specify multi time, only totals + various breakdowns. You would be better concentrating on meeting those breakdowns than 'just' multi.
Many of us were in your situation. Hell, I have well over 6000 hours, half of which is multi, and ATPs from Europe,. Austalia and the US and I still struggle to find the 'next step up'. It's a disappointing fact that no matter how many total hours you have, and no matter how many hours you have in any particular type, experience or skill subset, the next job you hope to get will probably want something more than you have and there will be someone else who has that tick-in-the-box ahead of you.
Better to bide your time accruing the right sort of 'other' hours until you meet some different operator's requirements who will give you the loggable time you desire for the next struggle up the career ladder. Meanwhile apply to everywhere you're prepared to move to and sidestep to them if they offer the time you need.