If they are otherwise healthy and not stressed by anything besides the boxwoods growing up close to them, they should respond well to the cuts you propose.

The point of cutting only one third of the branches close to the ground is to leave you something up top while the base fills in. You do one third a year so there is no ugly period of nothing as a complete rejuvenation pruning at one time would do.

With this in mind, the first year I would prune one third of each plant close to the ground- depending on structure leave maybe 6-10 inches. Then, if you want, top the remaining two thirds to give you something better to look at this year.
Next year do hard pruning on another third and top the remaining portion.
The third year do a hard prune on the last tall third and your 100% rejuvenation is complete.

After that just touch up yearly after blooming and learn how to prune to direct growth. Hacking haphazardly results in haphazard growth and with just an hour of study you can prune to improve the appearance instead of just to remove foliage.
Link below on pruning- everything you need to know is on this one page. Please read it!

Here is a link that might be useful: Proper Pruning Techniques

Pruning 1/3 per year is considered the absolute safest way to renew an azalea, but many don't have the patience to spread out the process over three years. Cutting them to within a few inches of the ground - the entire shrub - can be quite successful if well-established and healthy. Same for rhododendrons. While not without a degree of risk, many of us here have used the 'rejuvenation' approach.

Here is a link that might be useful: Earlier pruning thread