Was the ballast able to fit inside the ballast chamber?

Though I'm a tidbit mad because I glued the lampholder ever so slightly crooked... it irks me LOL.

Serves me right for doing this late at night...

Was the ballast able to fit inside the ballast chamber?

Indeed! A perfect fit; could likely squeeze in another right beside it... 

In this case, you actually need a second ballast.

Here is a link to a second identical ballast:

https://www.ebay.com/itm/334836555779

Are you sure this is teh correct ballast?
It saya 0.36A, but the PL13W is a 0.22A lamp (if I'm not mistaken), so it would end up overdriven...

So, Medved, if that's the case, then can I wire up two sockets in series and run it that way? Or still no.

And also, I noticed that these lamps are much brighter on this ballast setup than the one I have downstairs. I guess it's alright if lamps EOL quicker; I have about 5 of these 4100K lamps.

Are you sure this is teh correct ballast?
It saya 0.36A, but the PL13W is a 0.22A lamp (if I'm not mistaken), so it would end up overdriven...

Just so you know, this Philips spec sheet specifically states that a PL13 CFL lamp has an operating current of 0.29A, which is very close to that of a F15T8 fluorescent tube rather than 0.22A like you initially stated:

https://www.lighting.philips.com/api/assets/v1/file/PhilipsLighting/content/fp927902882766-pss-global/product_leaflet_caption.pdf

The series choke ballast that I recommended is appropriate because it drives PL13 CFL lamps at the rated 0.29A current since the line current on that series choke ballast is 0.29A whenever it is specifically connected to a PL13 CFL lamp since a series choke ballast without a PFC capacitor is the same as the lamp current. On the ballast label, the 0.34A rating is only applied when a F14T12 fluorescent tube is being operated on that ballast since a F14T12 fluorescent tube has a lower arc voltage drop compared to a PL13 CFL lamp and whenever you run a lower arc voltage lamp on a series choke ballast, the line current on the ballast increases. On the other hand, a PL13 CFL lamp has a higher arc voltage drop compared to a F14T12 fluorescent tube, which means that the higher arc voltage drop allows the PL13 CFL to be able to run properly at its rated 0.29A operating current.

See the ballast specifications on page 1-31 of this Advance ballast catalog:

https://s3.amazonaws.com/cesco-content/unilog/Batch5/781087/116417-Catalog.pdf

Here I couldbe wrong, indeed, the "0.22" I got from some ballast label here, but it could have been one of the underdriving ones.

However that Philips rating is very fishy to me, to the extend it ismaking me question the reliability of that publication.
The 56V arc voltage, with 0.29A current and the 13W power is just not adding up. Something is really off there, Unless tyey are counting on really very high crest factor (boosting the rms value up without transferring that much charge), which I doubt (Imean having the lamps formally rated for it with in a series choke, not that some cheepeese ballasts won't have that high crest factor).
The 13W and 56V would go more towards 0.26A (assuming sinewave current), not the rated 0.29A. So could that be a typo here?
Or the 13W
Or the 0.29A at 56V arc would lead to at least 14.5W. That does not match with the "power draw 13W" statement then.

And I would agree the last could be the case here, knowing how deceptive marketing poisoned the industry already long time ago. My guess is, because the true efficacy is lower than the rated 62lm/W, they designed the lamp for the higher power instead and and lie about the true energy consumption (and get away with it just because "it is within the allowed tolerance").

I recommend consulting with James on an answer to this question since he can better help to explain why a North American GX23 PL13 CFL lamp has an arc voltage drop of 56V and an operating current of 0.29A, but draws only 13W of power while an 18 inch (440mm) 15W T8 fluorescent tube draws 15W of power and has a nearly identical arc voltage drop and operating current (55V arc drop, 0.30A) compared to North American GX23 PL13 CFL lamps.

For your reference, here is where I obtained the 55V arc voltage drop and 0.30A figure for an 18 inch 15W T8 fluorescent tube:

https://www.scribd.com/document/110155293/Westinghouse-Guide-to-Fluorescent-Lamps-Brochure-1979

From my understanding, this power reduction from 15W to 13W while maintaining a nearly identical arc voltage drop and operating current is achieved whenever you add krypton to an argon-mercury discharge and reduce the tube diameter like you see with European 5 foot 65W T12 fluorescent tubes, 4 foot 40W T12 fluorescent tubes, and 2 foot 20W T12 fluorescent tubes being replaced with 5 foot 58W T8 fluorescent tubes, 4 foot 36W T8 fluorescent tubes, and 2 foot 18W T8 fluorescent tubes and being specifically designed to operate in existing T12 preheat fluorescent tube fixtures without any ballast replacements for energy saving applications and you can see that the North American PL13 CFL lamps have a smaller tube diameter compared to 18 inch 15W T8 fluorescent tubes.

In addition to that, James has some lamptech pages featuring these GX23 base PL13 CFL lamps that specifically state the figure that I pointed out from the Philips spec sheet:

http://www.lamptech.co.uk/Spec%20Sheets/D%20FLC%20GE%20Mod-U-Line13.htm

http://www.lamptech.co.uk/Spec%20Sheets/D%20FLC%20Osram%20DuluxD13LV.htm