To pick a nit, you'll have to log out of United and back in to see the miles present, so there's no need to try to be ready to transfer points and click Book on united's website simultaneously. The odds of the seats you want being taken in the 1 min between transferring and logging out of / into united.com is very low.

Also - no one mentioned, but if you book a United award as a round trip or open jaw, you can get a free "stopover" in the destination region (they recently changed the rules, but I think the way I wrote it here is pretty accurate as to the new rules). In other words, if you're going from SFO and want to visit Barcelona and Amsterdam, you can do as recommended and book SFO-AMS then BCN-SFO for 60k round trip. But for no additional cost* you can book SFO-AMS, AMS-BCN, and BCN-SFO for 60k round trip. For this specific routing, you'd likely have a connection between AMS and BCN, but that's fine (i.e., AMS-ZRH-BCN). This can also be booked on united.com. First search each piece as one way award and confirm everything you need is available, then use the multi city search, just as you would for open jaw, and plug in each 3 legs with their respective dates. Ignore the prices per leg as they can be wonky, but when you get to the end it will price at 60k, else you did something wrong routing-wise. You could even get more advanced and book something like SFO-AMS / AMS-FCO / BCN-SFO, and just pay for your own way from Rome (or wherever you choose) to Barcelona. That's 3 cities for 60k + taxes + a cheap flight.

*There is slight additional cost in the form of taxes for the AMS-BCN flight(s), but almost assuredly less than you'd pay otherwise to complete that travel. It would vary by where you connect, but likely be ~$50. For example, AMS-ZRH-BCN has $43 in taxes while AMS-VIE-BCN has $56.