One way to navigate a lot of tabs with Chrome on the iPad would be to somehow get a list of them out of the device, since this would then allow you to finally close them and start over. Using the list, preferably a clickable webpage, you'd be able to refer to the sites you want and click to re-open them as needed. The problem then becomes that with Chrome/iPad there's no obvious way to get a list of the open tabs either.
For that, a solution is that you can essentially "export" the list of all your open tabs by using Chrome Sync to synchronize the iPad to your Google account in the cloud. To do this, you have to authorize the Chrome browser itself to log in to your Google account. Don't head for a web page to do this; instead look in the Settings menu for Chrome itself. After you enter your Google account information, a sub-option for "Sync" should appear; swipe it for the detailed options and make sure the option to synchronize 'Open tabs' is enabled. Immediately, your iPad will upload the set of open tabs to your Google account online.
Ideally, now you'd be able to inspect the Chrome Sync data by logging into your Google account online—this time on the web—and viewing it in your Google account profile, right alongside the tons of similar tracking data you can find at https://myactivity.google.com/more-activity. You'd be able to browse this secure webpage with any device from anywhere and you'd even be able to use an iPad—such as the same one the data came from—to browse around and click.
Unfortunately however, it seems that Chrome Sync is a separate product that's not totally integrated with the rest of the Google data harvesting apparatus, so the only online hint that I could find of the data you captured is via the a single summary page https://www.google.com/settings/chrome/sync, which acknowledges the number of "Open tabs" that were synchronized, but doesn't seem to provide any way to actually list them (I did spend a long time searching to no avail, but since I always find the Google account pages entirely byzantine, it's still possible that the data is accessible somewhere).
In any case, failing the online option, you can still examine the "Open Tabs" list by using Chrome Sync in its intended way: on another device. Using a different, non-iPad machine, repeat the steps above to enable Chrome Sync and then go to the Chrome History menu. You'll see an additional section for your iPad in the pop-up menu, and if you go to the full page History view, you'll see a separate tab along the left margin which finally displays a clickable list of the open tabs uploaded from your iPad device.
This list is an HTML skeleton with most of its content generated by javascript. If all you want are the titles of the open web pages you can simply copy/paste from this page into any other app. But if you want the underlying URLs as well, you have a bit more work to do. You can either paste into an app (e.g. Microsoft Word) that supports a richer format which preserves the links—and where you know how to separate out the links, or use Chrome's Inspect Element developer features (or the [F12] function key) to grab the fully-resolved HTML after having been rendered by javascript.
Now having walked through this approach, I must confess that the procedure does not work for Incognito tabs, for the simple reason that those pages are specifically excluded from participating in Chrome Sync.
I thank @w3d for posting the question, and for his helpful answer too. Indeed I was already aware of the new thumbnail view feature in Chrome/iPad when I put a bounty on this question. That new view does not allow text selection or even displaying each site's URL, so they doesn't address my own specific need. In fact, since many of the tabs I'm trying to salvage are incognito, even the solution I describe here remains incomplete for me.
I'm still hoping someone will describe any way to manually export a URL listing of all the open tabs—including incognito—from Chrome on iPad.
