Techniques for digitally copying video laserdiscs
So, approaching this from a "top view":

A LaserDisc records analog signal. The recording process is basically:


Make a composite video signal (basically, PAL or NTSC "baseband")
FM-Modulate the 4-6 MHz wide video signal to a nominal 8.5 MHz (resulting spectrum somewhere between 7.5 and 9.4 MHz, iirc) FM-modulate your left and right Audio to 100 kHz wide carriers at 2.something MHz
Make a (weighted) sum of these signals, and just clip them: you get a PWM-alike signal, and that is used as land/pit signal¹
Digital data (especially: digital audio) is used as baseband signal and added (OR'ed, logically) to that. 


Let's first ignore the digital part: you can simply get it by low-pass filtering the signal and digitizing it with a threshold/1bit ADC, just like a CD.

So, you'd get the 2.something MHz to 9.4 MHz bandpass analog signal.

First observation: Ok, that's not that much bandwidth. Go buy a normal SDR peripheral that can do such "baseband-y" frequencies and just get over with it (e.g. USRP N2xx / USRP X3xx + BasicRX/LFRX daughterboard, connect your photodiode buffer output to that), instead of designing your own hardware. Do the signal processing in software. At these data rates, laptops will do that at real-time (i.e. full read throughput). 

Second observation: that is only ~6 MHz of bandwidth, and that's already a bit easier to convert to digital, if you wanted to go the DSP route on the signal – you can elegantly undersample that with a ~12 MHz ADC.

However, the resulting DSP necessary to re-arrange the spectrum inside your signal processing chain might not be trivial.

I haven't looked inside an LD player, nor have I read the patents, but I guess: the player uses analog bandpasses to divide the video from the audio, and analog FM demodulators to bring the signals back to baseband/usable format. You could then simply use stock soundcard and stock video card hardware to do what you want (but you'd still only have built an LD player without much long-term optimization, so this probably has little advantage over buying an LD player used). 

The fact that the signal got clipped is a horrible nonlinearity – but mathematically it mainly introduces new frequency components (for FM signal – for AM, you'd lose a lot more info!), which can be filtered out if you know the spectral support of the original signal.

Now, of course, you can do that in DSP, too. So: I like your idea of the "read 0 or 1 only, do signal processing digitally". Problem is that if you look at the signal that way, you're in for quite a complexity treat, digitally:

typically, the "digital" in DSP means "value- and time-discrete", and that time-discreteness simply isn't true here. So, you'd basically re-invent the delta-sigma modulator: You'd have a digital counter that runs at a very high speed, and each land/pit or pit/land transition is used as an interrupt to read the current counter value (representing the length of the last state) and reset the counter. Your output sample stream would not be constant-sampling-period amplitude-samples, but constant-amplitude period-samples – and that's something the math is taught much less in EE :) and thus, the availability of ready-to-use libraries, be it in digital logic IP or CPU software, is less astonishing than for "classical" DSP.


¹ I'm not even sure whether it's that signal, or whether that signal gets used as input for a differential Land/pit modulation – but that doesn't matter, as it doesn't change the structure of the read-out analog laser signal