How to shorten DNS propagation effect

Short answer: You can't.

Many DNS servers will have policies that override the TTL that you specify. By reducing the TTL, you are probably doing everything you can though.

This other question may be of interest to you:

The first thing to do is update the TTL in your domain's SOA record and make it much smaller say, 600 seconds (10 minutes).

IN  SOA     ns1.example.com.  [email protected]. (
                       2            ; serial number <<<<update this
                       3600         ; refresh   [1h]
                       600          ; retry     [10m]
                       86400        ; expire    [1d]
                       3600 )       ; min TTL   [1h] <<<<reduce this to 600 

Update the serial number to make sure that the changes are noticed.

This should reduce the TTL for your DNS records to 600 seconds but it will take up to the current TTL seconds for this change to be noticed around the internet.

Now when you change your IP address it should only take 10 minutes for it to be noticed. In practice though it can still take quite a long time.