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I play 5 songs that utilize different values for the same parameter of a particular preset. … Is there any way to send a MIDI command to the TimeFactor to set a parameter's value without using the minimum and maximum trick?

I have a sinking feeling that I'm missing something about your question here.  But you do have a Liquid Foot 12+ MIDI controller, and that's a more than capable device for this.  So, here goes (and forgive any misinterpretation or repetitive reviews on my part):

I'm working from an FCB-1010 with the PitchFactor, but the concepts are the same, along with the Eventide MIDI implementation.  You can set the parameter limits at the MIDI controller end, or the stompbox end (transmitting or receiving).  The results will be the same.  I'll have a 'bank' of 10 switches available, yet only one or two of those switches will send a Program Change message.

The remaining switches in a bank modify one or two parameters within that single stompbox preset.  I don't have to review the MIDI channel or system settings for you (from your previous posts).  Assuming that the CC numbers on the LF 12+ and TF match in terms of the TF parameter that you want to control.

There's a small range of CC values that will call up a specific TF parameter value.  For example (in the PitchFactor): with a 2 second delay range, a CC value of 64 calls up 238 ms.  If it's a 1.48 second range, a CC value of 64 will call up 206 ms.  Every TF parameter scales the CC value range of 0-127 a little differently, and that scale may change from algorithm to algorithm.

It does make sense: If a parameter has 6 possible positions, then the CC value range of 0-127 is divided six ways.  If there are 3,000 possible parameter positions (like delay time), then 128 CC values are only going to nail 128 of those parameter values.  Unfortunately (no TimeFactor here), I can't tell you what CC value or small range of values will correspond with your TF parameter.  It may help to expand on exactly what you want here (for example, you want to hit delay times at 250, 500, 1,000, 1,500, and 2,000 milliseconds).

Let me give you a small example of what I'm talking about.  This post describes the process of changing keys and scales in the PitchFactor.  It's all based on a single preset, with many parameter variations provided by the CC value messages.  I worked out the exact CC values by trial-and-error, then formulated a more efficient way to cover any other PF parameter.