The key to this solution is to use the Vref input of a suitable A/D converter in order to scale the input voltage. This is not an all analog solution; but unless your frequency, resolution and/or latency requirements are too restrictive ...
1) Use a differential amplifier to take the difference between Vref+ and Vref-. This will be the Vref input to an A/D converter with a suitable reference voltage range (possibly ADS7816 for example). The differential amplifier will need to scale the output so that it falls within the allowable Vref max and min range of the A/D converter. The use of the Vref input sets the full-scale value for Vin taking care of the division in your transfer function (A/D output at full-scale when Vin = Vref+, and at 0 when Vin = Vref-). Note that you may not find an A/D converter that allows a Vref input all the way down to zero, but the ADS7816 is specified clear down to 100mV (Vref range 100mV to 5V).
2) Use a differential amplifier to take the difference between Vin and Vref-. Scale this the same as the differential amplifier in step 1. The output of this amplifier is the voltage input to your A/D converter.
3) All that is left then is to take the output of the A/D converter, convert it back to analog with a D/A converter, and apply necessary offset and gain with an op-amp to achieve a 1-5V range (calibration pots may be useful). A micro-controller would simplify the interface between the two converters, but it really doesn't need to do anything but time the conversions and transfer the data.
One of the main advantages to this solution over reading Vref+, Vref- and Vin separately into an A/D converter is that this method utilizes the full range of the A/D converter (assuming same resolution in D/A converter) for the output regardless of how close Vref+ is to Vref- (within the Vref min limits mentioned above). In other words, the number of steps (resolution) for Vout as it ranges from 1 to 5 volts will be the full range of the converters. If separate conversions are used for Vref+, Vref- and Vin; the number of steps available for Vout will be limited to the number of steps between the A/D conversions of Vref+ and Vref-.
Since there is only one conversion per sample with this solution, you will not need to worry about sampling and holding all three inputs at the same time, or what errors may result if they are sampled at separate times.
Another advantage of this method is speed. Since the microcontroller does nothing but time the conversions and transfer the data, the main limiting factor is the speed of the converters. For other solutions, if the microcontroller needs to do math (especially division), that time would need to be considered.
A useful app note on using Vref for scaling: VOLTAGE REFERENCE SCALING TECHNIQUES
Analog Devices has a useful tool for designing and testing differential amplifiers HERE.
For greater accuracy and stability, you might consider using instrumentation amplifiers for your differential amplifiers.
Your compensation network is wrong.
As shown in the typical app in the datasheet, compensation should be done with a series RC block instead of a single resistor (R4 in your circuit).
Without proper compensation, the circuit will not be stabilized.
Best Answer
If the frequency was fixed, you could have used a LC resonant tank, but frequency is variable.
So, if you want to passively increase voltage on a signal, pretty much the only solution you have is a transformer.
Another solution would be to use switching converters to get higher DC voltages, and power your signal amplifier from these.
Both have merits in terms of size, weight, efficiency and cost.