Not attempting to hijack the thread here but seeing as I'm laid up post-surgery and bored out of my mind, I saw this and though I'd have a go at making an even simpler sweep generator as that retriggering seems very complex. Also I'm a cheapskate and didn't have any LM324's in or CMOS 555's which disappointed me.
Got this far. Excuse the codeine inspired artwork.
Could do with an opamp buffer on the output. Output voltage is about 2/3 VCC so use a 78L09 on a 12V supply and bob is indeed your uncle. Scales from 100mHz (milli not mega) to about 200KHz. Change the 560 ohm resistor to control sweep rate. Change capacitor to control range. Concept is about the same as the original one. I minimised the design from the original one and ended up here after an hour or so. And it worked!
Could do with an output buffer.
(also excuse the 5V in the diagram - bench power supply is too heavy to lug around so I used a phone charger)