How long is your piece of Tenex? If it is long enough for normal 2-fid buries, then forget the Brummels and make normal stitched eyes.
The method shown in banjo's link actually works very well. The tucks are, inch for inch, quite a bit more effective than a bury. The trouble is you don't know how many tucks you need to make up for X number of missing inches of bury.
The girth hitch is the worst option because the endless loop has the weakest splice structure. With spliced eyes you have all that friction on the ring surface helping to prevent the splice from sliding apart.
The girth hitch might be the best option if you centered the splice right in the middle of the hitch. This would be bulky, but the two buries would be sharply bent around the ring and this would strongly lock the buries in place.