1045 will not have excess carbides to worry about but it will have proeuctectoid ferrite (extra ferrite) to dissolve so while you won't have the same requirements in soak time for getting carbides, you will have some more austenitizing to get that ferrite into solution, this is why the iron-carbon equilibrium diagram (for steel) is shaped like a big "V" with the eutectoid (.8% carbon) being in the middle.
There should be no large or elongated grains from forging if one has done the process properly not to fall short of or exceeded the rate of recrystalization, and if they did - that is what normalizing is for.
Repeated cycling will refine grain, but once again that is what normalizing is all about. Refining grain is one thing, putting carbon into solution and refining carbides is another, and if one spends too much time heating and not enough time soaking, although there will be fine grains, there will also be large carbides and segregation, but then a lot of that is not as relevent with 1045. Cycling around and below Ac1 will tend to take carbon out of solution, heating closer to Acm (or in this case Ac3, due to that ferrite) will tend to put carbon, and ferrite, into solution. This is one of the biggest shortcomings of magic bullet recipes, steel is just too complex to obey our wishes for a magic cure all
So setting miraculous secret quenching techniques aside, 1045 is pretty simple stuff and I would say have a go at just doing it over to see if you can nail it better the next time with your only concern being a real buggaboo everytime you start unecesarrily heating the steel above critical- decarb

There is scant carbon there to begin with in 1045 so I would be very careful not to lose any more than I had to.