Would your front derailleur be able to shift onto the inner ring if it were 2mm closer in? (It just needs to miss. 3mm is way off.) It it can handle a shift further in, consider getting a Phil Wood bottom bracket. It is easy to dial in exactly the chainline you want.

I went Phil Wood when I went triple chainline on my Mooney to get three very different fix gear ratios. Being limited to a double sided track hub where the cogs are very close in relative to any normal, FW or cassette, I needed to move the crankset in as far as possible. My small chainring is 36 or 38 teeth and I have the chainline set so the 38 just about scraped paint. The setup has worked flawlessly.

Phil Wood has many choices for BB dimensions. You have a big selection of axle widths and they can start as symmetrical or their standard asymmetry or you can custom order (for I believe the same price, just a wait) any other dimensions you want. They are very knowledgeable and a joy to work with. (Number one, they are a machine shop, not a store. They keep on hand the units that sell regularly but machining anything else is what they do.)

Ben