I am a king with a castle but seldom a crown.
Perhaps because "an Englishman's home is his castle".
I am able, with but a single step, to assemble the peoples unto me.
That is, to GATHER them. (F to G is not only a single-letter change, but moves only one step along the alphabet.)
I am, with a change of heart, beginning to be softer.
...and FATTER. (As I failed to notice and Rubio pointed out to me in TSL, the right way to parse this is "with a change of (heart beginning)": i.e., the H changes.)
Give me an endless jet and make me soar.
Insert E (from jEt) making FEATHER, though personally I wouldn't exactly say that a feather soars.
Even when I have a rough start, I'll go the distance and then some.
You will, in other words, go FARTHER. ("R" is the start of "rough", of course.)
A new beginning lets me make alternate choices;
Which would you RATHER?
but if I then go left instead of right, I'll agitate myself into a frenzy.
No need to work yourself up into a LATHER about it.
Replace part of me and I'll at last relax, a worshipper of the sun.
You will, in other words, be a sun-BATHER.
Deus dedit nobis hodie. Carpe diem!
Well, today is FATHER'S DAY...