[Quantum`]

Many videos, especially higher-def ones, hang for as much as 30 seconds. 

Looking at the download bar it seems clear that the data is arriving in random bursts.

Aside from horse-whipping my provider (looking at you Frontier), are there other measures I can take?  I have fiber-to-the-home, 15MB.

[bry]

To receive meaningful assistance you will need to provide a full debug log.

The instructions are here... debug log (wiki)

If you are using the Basic Method, then ensure the following is applied...
1.Enable debugging in Settings>System Settings>Logging,
2.Restart Kodi
3.Replicate the problem.
4.Upload the log to Kodi Paste Site manually or use the Kodi Logfile Uploader. (wiki) With either method post the link to the log back here.

If you are using the Advanced Method ensure you have correctly created and applied the advancedsettings.xml file (wiki)

In both instances, you should see the word DEBUG throughout the log.

Note: Full logs only. No partial or redacted logs
Do NOT post your logs directly into the forum. Use the Kodi Paste Site. Post the link to your pasted log in the forum

[Quantum`]

https://paste.kodi.tv/izoxowonoq

[Klojum]

Many videos, especially higher-def ones, hang for as much as 30 seconds. 

I see only ComedyCentral addon related entries in your log file. Any other add-ons having troubles?

You also forgot to turn on debugging and restart the Kodi application for more in-depth logging details.

[Quantum`]

I realize that I am only supposed to pastebin the full log, but every pastebin I've tried says the logfile is too large. (1.4MB)

As an example, TV Land|Gaffigan is unwatchable.  Just a series of still images and no audio. (1080)

I can watch most 720 resolution shows without much interruption.

[Karellen]

Disable Update Library at Startup for both Videos and Music\
Once Debug Mode is enabled remember to RESTART

Try https://paste.ubuntu.com/ as they allow larger logs.