Hi Linda
It is a really hard search given the period that you are in and records not being available on line. Given the on line restrictions on Scotlands People, it is the kind of search that would normally be done at one of the genealogy centres in Scotland (such as in Edinburgh or Glasgow) where you can view more recent certificates on line from the GROS. Trying to do it just from the SP indexes and then ordering certs would be an expensive mad exercise to be honest

I get the feeling though that visiting one of these centres is likely not to be feasible.
The Ancestry scottish censuses index do the job well even without the original images. The main bit of info that is not included on the Scottish transcripts is simply maritial status (single, widowed etc), which is unlikely to be relevant up to 1901 for John Snr (even if he was married by 1901, you are likely to be able to see this from the household entries).
One other thing which I am not sure whether you have considered so far in your searches is the joy (pain!) of spellling variants. There will be a few; Mullen/Mullan/Mullin and also you need to consider possibly a Mac/Mc before the name...
Regarding the possible death on the CWGC site. I thought from what you said on the other post as background info that John Jnr and his wife divorced? If you know the year of birth of the last possible child born to John Jnr. this would help you with dates. Also the year of a remarriage for his wife (did she show as divorced on her remarriage or widowed?).
No anwers at at all for you, just some thoughts unfortunately.
Monica