"What would happen if I leave it out?"

You will not have a proper 'voltage divider' circuit.

" No power switch, but I can understand the omission, since this is supposed to be highly customizable. I have to pop the battery connectors to power down, but my enclosure choice makes that easy enough"

You could try a 3 prong switching jack that disconnects the battery ground when no cord is inserted.

Like pedals use.

The Line Out circuit uses 2 47K and 1 100ohm resistors for the summing network.
You can disconnect R155 and add a 100 ohm resistor to ground to get a separate feed.

Welcome to the place.

A little side note on the 'PEC' tone control module.

Interesting reading: 
https://thedhtsstore.com/blogs/news/35901185-vintage-components-the-pec-a-k-a-couplate-or-bulplate

https://hackaday.com/2018/09/12/whats-a-couplate-the-stepping-stone-to-integrated-circuits/

They are available but without a datasheet you can't tell what they include internally.
https://www.bing.com/images/search?q=vintage%20PEC%20module&qs=n&form=QBIR&sp=-1&pq=vintage%20pec%20module&sc=0-18&cvid=32AEF5EA2B4D4AC78A3DEBF5456076FE&first=1&tsc=ImageBasicHover

Interesting how Sprague refers to them as a "Couplate PEC BulPlate Coupler Module ".

Centalab also made them:https://www.bing.com/images/search?q=%20Couplate%20Info&qs=n&form=QBIR&sp=-1&pq=couplate%20info&sc=1-13&cvid=7DA336B3F1BF4308ADE01C1119A853F7&first=1&tsc=ImageBasicHover

I would not think that it's the battery's fault.
More likely it's the dc to dc converter.
Do you have access to a scope to find what frequency the hiss is?

Oh.
But the converter is what is making the pedals hiss?
Not the amp? (with the pedals powered from the converter)

https://www.vakits.com/14-watt-single-channel-audio-amplifier-kit-1344
Stupid question: why did you knock down the 12Vdc battery to 9Vdc?

To replace the ic properly the balls on the pcb have to be reflowed.
They make sheets of teflon with the correct spacing holes in them & you simply lay the sheet over the flattened balls apply flux and reflow the them.

What in the heck were they thinking when they chose that IC ?>>>?
Great for a cell phone but a guitar amplifier?
Come on !
Good job midibob!!

The Reverb not working could be a faulty wire or transducer in the receive side of the tank.

The Vibrato working means that the circuit for Chorus works.
What differentiates the two is the switch. (Chorus does not use the variable Depth and Rate)
I would suggest that you check that.

The Vox amp uses the TPA3091 D1 ball grid array ic (cute!).
Midibob chose to use the SSM2305.
The layout that he chose is directly off of the datasheet.
https://www.badcaps.net/forum/showpost.php?p=350727&postcount=33

It appears that you may have an Input Jack issue.
If the Mic Input works then the output stage is fine.
The 'daughter board' is meant to resolve an overall 'no output' issue. (blown output ic)

Can you supply a link to that limiter?

Marshall never was one to supply actual service manuals.
Schematic is all you get.