Can I control the "space after" the chapter number if it needs to be different than the space after the chapter name that way (with just a soft return), though?
(Also: I'd thought I'd had that pull quote after the chapter number [as I'd mentioned in my first message here], but it's actually after the chapter name.)

All four iterations need to be styled and managed separately, and then in concert. No small trick.
If you want a lot of control over the printed page, the two paragraph approach might be best. It gives you unlimited control on the print page but limits you to the two-line TOC display.
The single-Para Style, soft-return plus Char Style method means you have to juggle line spacing and then spacing below on the print page, which should be do-able. Leading is controlled, more or less, by the following paragraph, so if you have 36pt leading to separate the number and title, then 14pt Body text following will be as close as any bottom/top spacing allows.
This is 24/48 for the auto-numbered heading, with a following em space and 1pc space below, and 12/14 with 6pt bottom spacing for the Body:

Seems like that should get you where you want... or did I miss something?