A reaxys search reveals only two examples ever of the N-alkylation of indigo dye, which doesn't bode well...
One uses phase-transfer catalysis (NBu4I, aq. NaOH, in benzene) and iodomethane, and the other uses NaH, DMSO.
There are, however, many more examples of acylation, typically with the acid chloride and a pyridine buffer. Could you take this route, then try to reduce out the carbonyls afterwards? Maybe some chemoselectivity issues...