User blog comment:Cloudy176/Yet another blog post of Turing machines/@comment-5529393-20130410144320

For 46 states and 3 symbols, you can use the 2 state, 3 symbol busy beaver to print 9 )'s, then go directly to state 1, eliminating state 0a.  This evaluates the function starting from a 0 multiplier, which is the same as starting from a 1 multiplier with one head removed.  So starting from ))))))))) at state 1 is the same as starting from ) )))))))) at state 0a, and you get a number greater than f_{\epsilon_0}(5) > gongulus.

This method gets you a minimal improvement to the 48 state 3 symbol machine:  Instead of printing a _ at state 0a, print a (, giving you a string of 374676383 ('s which evalutes to more than f_{\epsilon_0}(374676379). I did say the improvement was minimal!