Is it possible for a Land Value Tax introduced together with compensation for landowners to still raise money for the government without homeowners with mortgages being worse off?

An idea which I had randomly stumbled upon after encountering the suggestion that an LVT might possibly need to be introduced together with compensation for landowners to be politically possible. Then I had thought that the government usually should be able to borrow at lower interest rates than homebuyers as they have a lower risk of defaulting*.

So, imagine the following oversimplified scenario:

There are homeowners with mortgages with a 4% interest rate; the government can lend under an interest rate of 3%.

An LVT is introduced which raises the tax bill of the median homeowner with 1000 LCU per year; the median homeowner also receives 25000 LCU as compensation for this. To avoid handouts to rich people who happen to be homeowners this is also the cap of the compensation.

The government finances this compensation by issuing bonds and thanks to their interest rate of 3% has to pay 750 LCU interest per year for every compensated median homeowner; 250 LCU less than raised by the LVT. The homeowners use the money to pay back part of their mortgages ahead of schedule with the result that they under their, on average 4%, interest rate have to pay on average 1000 LCU less interest on their mortgages, per year; exactly equal to what they have to pay for the LVT. Thus allowing the government to improve its income without indebted homeowners under the cap being worse off.

However, I wonder whether this analysis misses anything. I have multiple times encountered claims of 'look how great an LVT is', but this had been mentioned in none of them despite that it looks, to me, like something which is not that difficult to figure out. Is there then any drawback or problem I had not noticed or was this effect just too small to be mentioned by LVT proponents?

* I don't know whether that is an universal rule, but a quick search suggests that is the case for both my own country and also the USA and Canada.

NOTE1: I had already asked a comparable question a few months age; however, I had received no answers and thus thought to rephrase my question, to reduce the risk of potential misunderstandings, and state it again.

NOTE2: Also before somebody comes in with something like 'homeowners are already richer than average; they need no compensation', this post was not meant as a policy proposal, but as a thought experiment on whether that it is possible that the government could benefit from an LVT without indebted homeowners being necessary worse of, if there is a sufficient spread between the interest rates the government and homeowners could borrow at.