That video is fairly accurate in how this is done, used a lot of the lessons I've learned over three of the E-Series heater cores. Depending on the year I would renew the Quick Connect fittings attaching the heater hoses to the core even if it means standing the expense of factory hoses and fittings. These become brittle with age and almost regardless how carefully they're handled they can break during the core R&I or shortly after having it all back together. Hoses with those fittings already installed are available, I used Ford OEM because I'm a snob that way.
The white plastic QD clips holding the hose assemblies AND the o-rings should also be replaced at this time, again OEM. Dorman does make QD connectors which you use normal heater hose to make those connections---find them on the Dorman site.
They do make tools to aid removing the engine side Quick Connect fittings but honestly using the arc joint pliers as shown works well too---it was how I did my first one of these!
I remove the doghouse completely, consider removing the passenger seat including base if you're slightly claustrophobic as I am. This would require a T-55 PLUS insert bit and a medium-length 18mm socket. I add a bit of anti-seize on these fastener's threads for ease of removal once again if that should ever be necessary.
Otherwise for the most part the video here is as good a guide as I've seen on this task. FWIW the workshop manual calls for removing the entire dash board which takes quite a bit long than that 1.5 R&I time---up to 10 or more!
Feel free to PM me if that would be helpful----we could speak by phone.
Good luck with this!