The substrate is somewhat different than following (Indole) and the -NH derivative is highly air-sensitive; so I am worrying about hydrolysis followed by alkylation method.
For N-acylation & N-alkylation you can use haloesters and K2CO3 in Acetone & reflux for longer time , the yield is lower but the quality of the product is good.
You might hydrolyze your derivative in 2M water solution of NaOH with addition of smaller amount of tetrabuthyl ammonium hydrogensulphate /TBAHS/. Then extract the deacetylated product into CH2Cl2 solution of CH3-I /10:1 vol/vol/ , CH3CH2-I etc.. TBAHS - or sooner TBA+ should act as phase transfer medium. Deacetylated indol will pass into the oraganic layer during extraction and get alkylated. Arising HI should pass during extraction into the water layer and be neutralized with the base.
To obtain an alkylated derivative separate the organic layer, wash it with water, remove water and let the organosolvent removed via rotavap.
Note: this method works well with phenols and carboxylic acids, incl. those aromatic...In your case small traces of acetic acid might contamine the product.
I hope the procedure might work in your case, too. If it does, almost the whole alkylation would be performed in one wessel.
If solubility of your derivative in 2M NaOH is poor, it could be increased by addition of smaller amounts of methanol, ethanol or other alcohol. This should not influence the corse of alkylation makedly. I would propose the follwing modification:
1 step - hydolysis of acetylated compound followed with rotavap evaporation of alcohol /in N2 atmosphere to avoid oxidation.../.