Hmmm, I find it odd that one circuit has different characteristics from the other since they are identical for the most part.
The first has the second opamp used as a buffer, which shouldn't matter from taking the output from the first opamp (depending on the severity of the load impedance, which might be significant if there is substantial cable capacitance or load input impedance - this IS important).
The second has the second opamp used as variable feedback into the Twin T reference node as a "Q" modifier.
They both indicates the use of LM358 opamps, which, BTW, are not the best audio opamps. They are based on decade-old designs and you will be better served thru the use of modern opamps that are truly rail to rail, ESPECIALLY at the indicated 3.3 VDC. For a 358 type, which may have an output sourcing dropout of 1.5 VDC, you have at best 1.8 VDC of signal compliance which works out to 0.9 VDC peak and 0.64 VDC RMS.
The performance of these opamps will vary depending on their open-loop gain bandwidth products.
What can I do to widen it slightly or make the center adjustable?
The way that you widen the response is to vary the tuning of each half of the Twin T (to a minor degree). When you widen, you loose depth.
The way that you adjust the center frequency would be to adjust the Twin T frequency setting components which are C69, C70, C15, C16, R7, R8, R9, and R10. Since adjustable capacitors will be an issue, adjust the resistors. this can be done by replacing each one with one that is 95% of the value in series with a trimmer resistor that is 10% of the value (9M5 and 1M trimmer). Of course, the two 10 M in parallel works as a 5 M.
I see that you specify 1% capacitors, but, assuming that these are NPO or COG, at 10 M Ohm resistor values, any leakage or even skin oil will dampen the responses.
You appear to have some significant notch depth and narrowness on the Hi-Q filter, especially for one opamp. What are you using for your calculations (it looks like Excel)?
I might suggest that you try pSpice since it is designed specifically for such uses.
Would a 9.76M resistor with a 500k 5% pot be better?
"Better" is a perception thing. It will make the adjustments twice as easy to do accurately (with them there little screwdrivers) while reducing the range of adjustment by 50%.
Why do you get the same output level with different input signal levels as a function of supply voltage?
If the circuits were working identically at either supply voltage, I would expect the same RATIO of gain regardless of supply voltage ("working properly" meaning within supply-allowed signal headroom).