In addition, I have used this same process for many homebrew monsters at my table and have never had a problem with it, so in my experience the technique is safe and effective.
Meaning, your process should give you a reliable CR with very little effort, even if thorough playtesting might "game feel" it to be 1 or 2 steps higher or lower. However, with the process you describe, since the effect on the math should be negligible and since the published monster has already included any "game feel" balancing the designer thought necessary, you should end up with an adjusted CR that isn't problematic, pending your own "game feel" assessment. Most of these "game feel" adjustments can be intuited by checking the Monster Features table later in the same section, and you should confirm that your monster doesn't have a feature with a tier-dependent adjustment in this table (such as Relentless or Undead Fortitude) or else take that into account if it does. (This is why there are so many questions on RPG.SE asking for CR verification for specific published monsters.) For that reason, you shouldn't feel beholden to the math regarding the CR calculations they will always be nothing more than estimates.
Most published monsters seem to involve some amount of "game feel" balancing based on designer's intuition or playtesting rather than following the calculations directly. These "game feel" assessments should occur when crossing between CR's 4 and 5, CR's 10 and 11, and CR's 16 and 17, corresponding to the boundaries of the player tiers, due to conditions, spells, or instant death effects that may be impossible to deal with at lower levels or trivially easy at higher levels. Then, barring any independent balancing steps you as the DM might deem necessary due to "game feel", the math should work out correctly. The math is reversed when sliding to a row of a lower CR.
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