Having had a recommendation from another SoR user then I have bought, and really like, the Saleae logic analyzer. See http://www.saleae.com/logic/
. Its about(?) the same price and gives lots of features - it understands various bus standards like I2C, Serial, TWI etc etc. Its also really small. You could certainly use it to measure timings in the UART comms.
The down side is that it only does 'logic' (ie 0's and 1's - not analogue voltages like the one you've found) - but can therefore produce more samples per second with less storage.
I found various far-Eastern suppliers who have produced 'pirated' hardware versions themselves dirt cheap, as you can download the software for your pc/mac/'nix box from the Saleae website (I'm sure Saleae will stop that soon!). But to my mind that's theft - so I bought an official piece of hardware. No - this is not an advert! If it helps - I'm based in the UK and it was delivered in 2 days.
I'm sure that your device is equally up for the job but would rather not be the one to choose how you spend your money!