How to convert 12 V DC to 12 V AC 50/60 Hz PSW?
Talk to the factory

Tried up to 17 V DC to take the sinewave peak into account.

Not surprising, 17 VDC is a very different customer than 12VAC RMS, with twice the overall power into a resistive load.
I also violently disrecommend &quot;trying&quot; anything on either a) AC mains or b) prohibitively expensive components. Do the research to exhaustion, then act based on facts. To misquote Yoda, &quot;there is no 'try'.&quot;
Since these lights are expensive, they ought to be well-supported.  A phone call to the factory for advice should really be your first stop.  I bet they can either give you a &quot;How&quot; or at least, a &quot;why not&quot;.  They might give you something out of left field, like &quot;We make 'em in DC too, the only difference is a $21 module we can sell you.&quot;
But your idea is a good one.
And closer than you think.  It's not &quot;all on you&quot; to make the perfect sinewave; you only need to get into the ballpark and let a transformer clean it up further.
If you can run it through an isolation transformer, you don't even need to really be all that sine-wave-ish. Because having a transformer in the stage will tend to clean up the sine waves and block HV chatter. (at the expense of the suppressed harmonics* heating up the transformer, so you'll need to derate it so it can stay cool). Further, the transformer removes any need for your switched output to even go negative!  You could make a sinewave that is 0-12V peak-peak (so 4.24VAC RMS with a +6V bias).
Feed that into a 4.24:12V transformer and you'll have a respectable true 12VAC coming out the other side.
If you can't find that size remember you can use two transformers back-back, with primaries connected to each other.  Clever selection of primary:secondary ratios can get you all sorts of places.  You just need to make sure you are within the transformer's current limits for each section. So on a 500 VA transformer with a 120V primary, that section is rated for 4.16 amps etc.

* When a sinewave is less than perfect, that acts as harmonics. Read all about Fourier Analysis to understand that.  Transformers are tuned for a particular frequency and will resist passing other frequencies; that's how transformers clean up dirty power.