The VFD can operate in "constant torque " mode if the motor is designed for VFD operation (because of both voltage and current (heating) requirements needed to accomplish this). However, you can set the VFD to run with a standard 3 ph motor, and you can set it to run just like a DC "servo" with an external (foot) speed control. I have a 1 hp, 3 ph, 230 VAC, 1725 rpm motor to which I added a 5:1 gear reducer, and then did a further reduction through the pulley, giving about a 7:1 total reduction. I made a foot control (could have bought one, but had what I needed to make one) and can vary the speed from 0 to about 240 strokes per minute (which totally suits my needs). With the reduction, the motor is at ample speed at low strokes per minute to prevent any over-heating and there is ample torque to sew 3/8 leather. If by chance I need to go faster, I can reset the upper frequency limit in the VFD and drive the motor in "constant hp" mode (lose some torque) and move along, for example on thinner, garment material.
My point is that the VFD is as versatile as a DC drive if set up properly. I am not that familiar with the so-called DC servo's sold for sewing machines, but unless there is some sort of feedback from an encoder (which I tend to doubt because of their low cost), it is not a true "servo" but merely a "variable speed" DC drive. So again, the VFD, I believe, is a viable option, especially if you already have the motor, which the OP does have. The DC servos that boast needle position capability, I assume, do have some form of positional feedback encoder or sensors, and would be more inline with a true "servo" system.