I have with me an incandescent light string. It is quite bright and gets warm. I don't expect the lamps to last long at all, a few hundred hours will be plenty, but that is expected for a generic $0.75 string.

When connected in series with an 11W PL ballast, it becomes dimmer and shifts into a deep amber shade, which is very pretty . I have some questions about this though:

• How safe is it to use a magnetic ballast with a resistive load, and could it be damaging to either?
• Will this really extend the lamp life following the V^-13 formula?

TIA

Yes it will extend lamp life, however ballast life is a different concern. 11W PLs draw 155mA, and if your lamp string draws more than that it can harm the ballast. I'm thinking the light string probably doesn't draw a lot but the only way to tell is to measure. Assuming the current is all good (less than or equal to 155mA) then I see no problem at all.

What is the current rating of the string? If 0.3A or below, I wouldn't be that much concerned about the ballast, the current would drop significantly (I would expect down to the 0.15A ballpark)
You may measure the voltage across the lamps, if it is 70V or above, the ballast is definitely safe.
Or other option (what I use on mushroom christmass lights) is just a diode in series with the string (across a switch bypassing it, so offering "normal/low" brightness settings).
And if you happen to use two strings of the same rating, you may just reconnect them in series for "low"...

The string probably and most likely doesn't consume 300mA or ~70W, it looks closer to <30W or at the most 40W.
Here's the measurements:

• across inductor - 195V
• across lamps - 145V (>70V)

Diodes do work but probably won't get this dim, plus a ballast is really fun to use with incandescents  . I tried two strings in series too but they end up way too dim for my liking.

The current ballast I'm using is by philips and is rated for 7/9/11W PL-S lamps on the cover but came with an 11W lamp so I'm treating the highest value as nominal. Would upgrading to 13W do anything advantageous? The current one doesn't seem to be getting warm at all.

You can use a dimmer to dim your string.