None of these are that foreign to your Experience Guy(s)!
i'm thinking if the second story of turns, reverses direction, and both ends end up, coming out on the same side (like a loop chord choked 2x around host neatly is also a prusik), with a straight, rather than slanted (slanted denotes clove/TL) 'bar' is an open prusik.
Placing an eye in the free end, and connectiong to saddle, would make a closed prusik. Or a closed loop of chord tied in circle to it's self, can be choked 2x, then connected to saddle for prusik.
Same knot as open prusik with 1, lower ring, and 3 top, in a closed formation (eye connected to saddle on each end); -like steal one ring from bottom and place on top story, you have a Schwab Prusik, better yet! Minimal change!
Prolly, the best in this , just one step off the path of experience is to take that double eye tail, and make your ol'TL; drop 1 ring from the bottom, and give it to the top(parallelling such action as in Schwab, only here with clove type lacing family pattern), hook both eyes to the saddle, and you have the Distel.
Just like that prusik; all just ~(about) 1 step from what your used to in most of them! But, i think it is such that the change in the mechanichs of how it serves you can be dramatic. Some take a lil'experience for you to naturally tune it in etc. This is good practice for if ya ever later step up to the VT, it can really take some tuning to ya.
But like any other better crafted machine, what a ride when ya get it going right!
All these friction hitches, can be made in 1/2", so ya might be able to experiment; without the variable of getting used to looking at that lil'chord etc. All of the 'closed' hitches would be inherently stronger compared to the 'open' tail on end of fritcion hitch. If the open system systems, could be compared to a choke (in sling lingo), and the closed systems then is a basket type position of the same line. For slings the ratings are usally Choke Strength x 2 1/2 = Basket Strength.
If ya gots some 3 strand, i think that is better/longer lasting tails/lanyards than braid on braid IMLHO. i think it flexes around host line nicer, and possibly that the 'flutes' between the strands allow better heat dissipation, than a 1/2" braid tube on a braided line, with more 'total contact' on the host line from the tube rather than 'fluted' contact point by 3strand. but, that is just a theory of why it seems to last longer.
So, nothing that far from home, here for ya to reach to and get a taste; see if it is for you. Of the 4 here : TL, Open Prusik, Schwab, Distel; i think the concensus would be to go for the Distel for best grab/release of the set, and a fairly close to an olde familiar form.
-KC