How about abolishing language police and introducing free Latvian courses instead
There are free language courses (and in Russian schools 60% of lessons should be in Latvian).
The problem is with the biggest carrot - Russia and its propaganda:
"Latvia is a failed state",
"Latvians are fascists",
"Latvians cannot govern themselves properly",
"It was a mistake to secede from USSR",
"wait a bit and you will receive citizenship and Russian as an official language (so you will not have to learn Latvian)".
And open border with Russia for non-citizens also is a good reason remain non-citizen.

How about tax deductions - the higher your level of Latvian (B2, C1 etc.), the lower your taxes?
That is a quite radical proposal - I haven't heard anything like that even from Latvian nationalists
because their representatives are excluded from the government
If you mean Harmony centre - they were excluded because their economic policy was incompatible with that of current government.
(the same way democrats or republicans exclude each other in US).
And they refused to sign government declaration, which contained things like:
"All government parties recognize that Latvia was unlawfully occupied by Soviet Union"
"Latvian should be only official language in Latvia"
In 2010 they also had to agree on similar declaration - and they refused.

The authorities apparently gave them no other chance to be heard
10 000 citizens can submit any bill to the parliament.