Tight money does not raise interest rates, at least over the relevant time frame for welfare considerations. Interest rates in the Euro zone today (0.5%) are almost certainly lower than they would have been had the ECB not adopted a tight money policy in 2011, raising rates from 0.75% to 1.25%. That policy drove the Euro zone deeper into recession, pushing rates even lower. The same thing happened in America in 1937-40.
Low rates can reflect tight money. Even low real rates. The low real rates in America today partly reflect the recent recession, which was caused by ultra-tight monetary policy in 2008-09.
Savers might also be helped by a lower rate of inflation. In practice, savers are hurt more by the drop in GDP [and real interest rates] associated with tight money, than they are helped by the lower inflation.
Thus the central bank should not help virtuous savers, nor should it try to help non-virtuous savers. But the tax authorities should help both groups, by eliminating all taxes on investment income.