These are approximately equivalent.

2 Skill proficiencies are more useful than a language overall (both in my experience and according to the rulebook in so far as you can train languages, but not skills, with the Downtime rules in the Player's Handbook), so you have to be careful, but losing your choice of a cantrip for one of the least useful ones (in my experience) should account for this discrepancy.

This can also be seen by comparing the Half-Elf and High Elf racial traits side by side (as these official races are roughly balanced with each other).

">" is slightly better than; ">>" is noticeably better than; ">>>" is much better than

\begin{array}{rcl} \bf\text{High Elf} & & \bf\text{Half-Elf} \\ \hline \text{+2/+1 ASI} & \text{<<} & \text{+2/+1/+1 ASI}\\ \hline \text{Fey Ancestry} & \text{=} & \text{Fey Ancestry} \\ \hline \text{Darkvision} & \text{=} & \text{Darkvision}\\ \hline \text{Extra Language} & \text{=} & \text{Included}\\ \hline \text{Keen Senses} & \text{≈} & \text{1/2 Skill Versatility}\\ \hline \text{Cantrip} & \text{>} & \text{1/2 Skill Versatility}\\ \hline \text{Trance} & \text{>} & \text{none}\\ \hline \text{Elf Weapon Training} & \text{≈} & \text{none}\\ \hline \end{array}

I consider Keen Senses and "skill of your choice" to be roughly equivalent since Perception is one of the more useful skills available from experience and WoTC Adventure Module analysis. Elf Weapon Training is a very minuscule benefit.

Now let's take your Sun Elf Homebrew and compare it in the same manner.

\begin{array}{rcl} \bf\text{Sun Elf} & & \bf\text{Half-Elf} \\ \hline \text{+2/+1 ASI} & \text{<<} & \text{+2/+1/+1 ASI}\\ \hline \text{Fey Ancestry} & \text{=} & \text{Fey Ancestry} \\ \hline \text{none} & \text{<} & \text{Darkvision}\\ \hline \text{none} & \text{≈} & \text{+1 Language}\\ \hline \text{Noble Heritage} & \text{<} & \text{Skill Versatility}\\ \hline \text{knows } light & \text{>} & \text{none}\\ \hline \text{Trance} & \text{>} & \text{none}\\ \hline \text{Elf Weapon Training} & \text{≈} & \text{none}\\ \hline \text{Celestial Resistance} & \text{>>} & \text{none}\\ \hline \end{array}

This hinges on the fact that Necrotic and Radiant are rarer damage types in your setting and that History and Persuasion are not used more often in your campaign. In a setting with heavy intrigue and/or many creatures that deal Necrotic or Radiant damage, this race may be unbalanced as Celestial Resistance is pushed to much better than status and/or Noble Heritage is roughly equivalent to Skill Versatility (I've not done any analysis on the proportion of campaign-styles where this is relevant like the WoTC balance team likely did, so I can't say for sure if this is balanced overall, but it seems to be).

This seems balanced

You have done an excellent job of identifying the potential issues with your homebrew. I can see no reason why you can't use it for playtesting. It is certainly a power-positive change over the standard Way of the Kensai monk. However that tradition is typically underpowered to begin with so this bring it back into line with the other traditions.

Are there any loopholes, ambiguities or other issues in the wording of the class feature?

Feature is fairly well worded, I can only spot one potential issue. It is something you have already partly identified and would probably make a sensible ruling on the first time you encounter it. How does the damage die relate to magical weapons?

This special attack must use your Martial Arts die for damage, even if the weapon could normally use a larger damage die.

As you already identified this feature synthesizes well with magic weapons that deal additional damage. Is the intent for this to replace only the primary damage dice or all of them? For instance; if I had a Frosthammer that dealt 1d10 Bludgeoning + 1d6 Cold damage and had a Martial Arts die of 1d8 what would be my damage roll with this ability? 1d8(B) + 1d6 (Cold) or 1d8(B) + 1d8 (Cold)?

Is the modified subclass still reasonably balanced relative to other Monks in terms of combat effectiveness?

If anything this change makes this tradition more balanced than it was. Way of the Kensai is weaker than the other non-spellcasting traditions anyway. This change is likely something that should have been there all along. Potentially your concerns about magic weapons will lead to it being overpowered but that will entirely depend on the available of magic items within your campaign.

Would giving up any of the standard Kensei (or Monk) class features bring the balance back into line?

I don't think this is necessary as it is mostly already balanced. But if you do find in playtesting that it is stronger than expected any of the suggestions you make could be a good fix.