Microcontroller with ADC and capable of SPI communication
Wow. 500,000 Samples/s ( aka 500 kSamples/s) at 10 bit resolution is pretty quick. I suspect any processor that has an ADC that can do this can easily handle the SPI data processing required.
SPI is a perfectly fine choice for transmitting at this data rate over a few inches.

stand-alone ADCs

Is there any reason not to use a stand-alone ADC for this application?
(These SPI ADC chips require some other chip to act as a SPI master. If your UWB chip cannot be set up as a SPI master, then none of these chips will work with it -- skip to the next section).
It's pretty easy to use the parametric selection tool at Newark or Digikey to select "at least 5,000,000 Samples/second" AND "at least 10 bits/Sample" AND "SPI". The results include dozens of chips such as


Linear Technology LTC1197LCS8#PBF : ADC, 10BIT, 500kSPS, SOIC-8, SPI
National Semiconductor ADC101S051CIMF : ADC, 10BIT, 500kSPS, SOT-23-6, SPI
Texas Instruments ADS7884SDBVT : ADC, 10BIT, 3MSPS, SOT-23-6, SPI
National Semiconductor ADC124S101CIMM : ADC, 12BIT, 1MS/s, MSOP-10, SPI
National Semiconductor ADC122S101CIMM : ADC, 12BIT, 1MS/s, MSOP-8, SPI


A stand-alone ADC will be smaller and conceptually simpler and probably lower power than a processor with a built-in ADC.

processors

There are quite a few processors that can handle 500,000 Samples/second at 10 bits/Sample. Alas, the parametric selection tools don't make it easy to sift out those that meet that requirement from the vast majority or processors that don't quite meet those specs.


All the chips in in the 8-bit AVR Atmel Xmega AU series, such as the ATxmega128A4U, can sample at 2,000,000 Samples/second at 12 bit resolution.
Many in the "32-bit AVR" Atmel AT32UC3C series, such as the AT32UC3C0512C, can sample at up to 1,500,000 Samples/second at 12 bit resolution.
Many in the 32-bit ARM NXP LPC series, such as the LPC1347FBD48, can sample at 500,000 Samples/second at 12 bit resolution.
Many chips in the 32-bit ARM Cortex-M3 Atmel SAM3S series, such as the SAM3S1A, cam sample at 1,000,000 Samples/second at 12 bit resolution.
Many chips in the 16-bit Microchip dsPIC and PIC24 series, such as the PIC24FJ64GB002, can sample at 500,000 Samples/second at 10 bit resolution.


video transmitters

Transmitting video wirelessly is more-or-less a solved problem.
Perhaps getting some off-the-shelf "tiny video transmitter" and matching receiver will allow you to get something working weeks earlier, letting you focus on the parts of your project that are not "solved problems".
Then later, after the rest of the system is starting to work, you could experiment with building a video capture/transmitter system that is lower-power or better in some other way.