I can't access the full article so I don't know if it relates to phenols.
Interesting that it is using both acetonitrile and water together. This might overcome your solubility problem. Hard to know without seeing the whole article.
If your phenol is appreciably acidic then your could try using a neat organic base like pyridine or ethanolamine, the solubility should be high enough to get the reaction going, and with any luck the silylation will pull your compound into solution.
DBU/DMF may also be worth looking at under the sample principle.
R3Si-OTf is one of the stronger silylating agents.
In our lab we try to avoid using aqueous media for silylations. Silicon has a "thing" for oxygen so your silylating compound might be converted into a silanol. Why not use a mixture of EtOAc and and a non-polar solvent that doesnt have a "free" oxygen? THF maybe?