How rule 110 would be proven to be universal if the tag system did not exist?
More a bunch of references than an answer ....  :-)
As said by @vzn in its comment Cook's proof is very complex and required a lot of work; nevertheless the universality of rule 110 renewed the interest on small model of computations.

Among the most notable results was the proof that rule 110 can simulate a deterministic Turing machine efficiently, i.e. with only a polynomial-time slowdown:


Turlough Neary, Damien Woods: P-completeness of Cellular Automaton Rule 110. ICALP (1) 2006: 132-143
Damien Woods, Turlough Neary: On the time complexity of 2-tag systems and small universal Turing machines. FOCS 2006: 439-448


Along the direction of a simplified/different proof of the universality of rule 110, you can find some work, e.g.:


Richard G.:  Rule 110: universality and catenations. In: Durand B
(ed) Proceedings of the first symposium on cellular automata "Journees
Automates Cellulaires", pp 141-160 (2008)
Juan Carlos Seck Tuoh Mora, Genaro Juárez Martínez, Norberto Hernandez-Romero, Joselito Medina Marín: Elementary cellular automaton Rule 110 explained as a block substitution system. Computing 88(3-4): 193-205 (2010)


For a good survey on universality in cellular automata and other ideas for proving universality:


Nicolas Ollinger: Universalities in Cellular Automata*. Handbook of Natural Computing pp 189-229


Finally a *personal* idea on an alternative approach that could be investigated:


Proving universality of larger CAs (with larger neighbourhood or more states) is much easier and you can even get rid of the intermediate tag-system simulation, so you could investigate if using rule 110 gliders it is possible to simulate an arbitrary larger CA; a slightly similar approach has been used by Nicolas Ollinger and Gaétan Richard in A Particular Universal Cellular Automaton to prove the universality of colliding particles systems (they prove that a particular system can simulate an arbitrary CA)


And don't forget that instead of working on a different proof for rule 110 universality, you can work on the open problem  regarding rule 54 ... is it (weakly) universal ? :-)