Just take them out, rotate them 90 and put them back in, this could be your done.

 

Thanks for the tip, but they are pretty done. We've tried pulling them and repacking them, but they aren't operating smoothly and one even has some play in it.

 

I believe your father-in-law has the 2013 Project California R5ca, which was alternately called the Rca. Cervelo maintains a comprehensive bike archive page with specs – the only other R5ca listed was manufactured from 2010-11. All of the R5s (R5, R5ca, RCA) from that time period share the same headset specs, but I'd reach out directly to their support team if you have any questions sourcing the bearings. It was a $10K frameset – I imagine a bit of advice comes with that price tag.

2013 Rca (click on the headset button):
RCA RIM MK1

Cervelo bike archive page, where you can find all versions of the R5 listed:

Bike Archive

Product support and information for past and present Cervélo bicycle models.

www.cervelo.com

This retailer lists the specs for the Cervelo bearing kit they sell for 2012-2017 R2/R3/R5's, but they're located in the UK. You might have better luck sourcing them from a US retailer.
Cervelo R2/R3/R5 2012-2017 Headset Bearing Kit

In the U.S., R&A Cycles is a larger Cervelo dealer and still has a NOS RCA, so they might be able to help you:

Cervelo RCA Frameset

The Cervélo RCA Frameset is the next step, the R5ca of today. Cervélo's "Project California" might still have that name, but it's now a full-time skunk works operation, figuring out how to take their best to the next level. The excuse is that the people here work in conjunction with the pro team...

racycles.com

 

Here's a screen grab from Cervelo's site:

 

jta, you're the best. Thanks so much for all the information. After consulting the bike archive, it turns out his frame is a 2011. The headset bearings appear to be identical to the 2013 model, though. Pretty rare bike. I got his frame from a retired pro, living in a basement, never built, for $2,700 in 2013. Right place, right time, right guy, I guess. Thanks, again, for all your help!