I don't have any access to /proc [...] 'man ps' mentions needing procfs mounted [...] I think just adding "ps" output to the existing "top" output would be one of the next steps.
If top took 5.5 minutes in showing output between two given snapshots above, I think adding ps won't improve the situation because ps data won't be correlated at all with top's. My bet would be to play with ps o argument, which allow you to get the information of top and more. Setting PERSONALITY to "bsd" on this Linux machine allows me to run ps as I were on a FreeBSD. I hope...
$ PERSONALITY=bsd ps faxo pid,euid,egid,ni:2,vsz:6,rss:6,pcpu,pmem,sta
+t:3=ST,tname:6,stime,bsdtime,args
PID EUID EGID NI VSZ RSS %CPU %MEM ST TTY STIME TIME C
+OMMAND
1 0 0 0 1924 652 0.0 0.0 S ? 19:24 0:00 i
+nit [2]
2 0 0 19 0 0 0.0 0.0 SN ? 19:24 0:00 [
+ksoftirqd/0]
3 0 0 -5 0 0 0.0 0.0 S< ? 19:24 0:00 [
+events/0]
[...]
1368 111 111 0 26580 912 0.0 0.0 Ssl ? 19:26 0:00 /
+usr/sbin/ippl -c /var/run/ippl/ippl.conf
1423 0 0 0 4800 1608 0.0 0.1 Ss ? 19:26 0:00 /
+usr/lib/postfix/master
1428 101 104 0 4812 1604 0.0 0.1 S ? 19:26 0:00
+\_ pickup -l -t fifo -u -c
You can s/args$/comm/ in order not to show parameters of commands:
1368 111 111 0 26580 912 0.0 0.0 Ssl ? 19:26 0:00 i
+ppl
1423 0 0 0 4800 1608 0.0 0.1 Ss ? 19:26 0:00 m
+aster
1428 101 104 0 4812 1604 0.0 0.1 S ? 19:26 0:00
+\_ pickup
HTH.