I find the idea of an SSB repeater quite challenging.
A repeater has noteworthy the function of allowing communication between points which are mutually inaccessible along the direct line.
A repeater has not the function of giving the word (the channel) to one sole participant a time (sic!). I greatly prefer the convivial chat in SSB on the HF bands to the scholarly sequenced conversation in FM on 2m and above!
Therefore, the SSB repeater would just be a continuously operating frequency translator, installed at a high place, which takes in a first, lower frequency band, e.g. a 12kHz channel at 434MHz, and gives it out, transposed and amplified, in a higher frequency band, e.g. at 439MHz.
For putting this in place, two problems must be solved:
1) to achieve an amplification of 90dB without feed-back, and
2) to achieve steep (rectangular!) channel filtering to avoid crosstalk.
The solution to the problem is in the combination of a digital I/Q receiver at the first, lower frequency, e.g. based on the Realtek RTL2832U chip, with digital filtering, amplification and processing to isolate the 12kHz baseband signal, and reemitting the baseband signal at the second, higher frequency with the help of an I/Q switching modulator, followed by a HF amplification stage.
The advantages of passing through the baseband are a) the distribution of the necessary gain stages between three different frequency levels, reducing possible internal feedback problems, and b) the ease of realizing a very steep and phase-linear filter window for the 12kHz channel.
The advantages of digital signal processing are the ease of realizing time-delayed phase-linear FIR filters and the total avoidance of external feedback by an appropriate combination of time-delay between input and output signal, and high-pass filter cutting off all low-frequency signals beyond the time delay of the signal processing chain.
Input and output frequency may be in the same, or preferably in different bands.The operation on the repeater is as ordinary operation, but in duplex.The repeater processes any type of analog or digital input signal and any type of modulation to the frequency-translated output.
Remains the question whether such repeaters are admissible after all, because they work in continuous operation, monopolizing one channel (the emission channel) from the band.However, this might be worth the value of providing a real chatting option in SSB or CW via a repeater. Furthermore, if there is no activity on the input channel, the output is silent, too.
In any case, HAM radio is an experimental discipline, and this would certainly be a field of new experience, which is worth the effort!