The rules don't really work together

Let's start with retraining (PHBII page 191). It cannot change your class levels - for that, you need rebuilding (PHBII page 196).

However, you cannot rebuild a monster class, because Savage Species page 152 says:

A monster may not multiclass until it completes the full progression of its monster class.

As soon as you "trade out" any monster class levels, the only thing you can replace them with is the same levels you just gave away. So no, you cannot just dump RHD and put class levels in their place. You could use the rebuilding option to change your race, but that removes the benefits of your old race as well as its RHD and LA.

There are monster class rules in other sources, most notably the Savage Progressions archive on the Wizards of the Coast website. Those rules do let you multiclass, but this brings with it another issue - you lose the monster's abilities when you trade out the levels that gave them to you.

Since level adjustment buyoff only works on class levels, not RHD, you will have a lot of difficulty buying off LA if you can't get rid of RHD.

Once the total of a character's class levels (not including any Hit Dice from his creature type or his level adjustment) reaches three times his level adjustment, his level adjustment is eligible to be decreased by 1.

But there are other rules that can help you

Since monster class rules are unfriendly, we can ignore them entirely and just take a typical monster without a monster class, but with an LA. The monster then goes on a night out and meets a fellow succubus, who hits him with a bunch of negative levels. In 24 hours...

If a negative level is not removed before 24 hours have passed, the affected creature must attempt a Fortitude save ... On a failure, the negative level goes away, but the creature’s level is also reduced by one.

After becoming a creature with 1 RHD and however much LA, the monster embarks on an adventure to gain character levels the old-fashioned way. With many fewer RHD, it will also be easier to buy off level adjustment (though you can't buy off more than 3 LA before level 20).

If you can meet the prerequisites of prestige classes by your previous gestalts, than it is reasonable to take Beastmaster as soon as possible. I assume you are going to finish your Convoker advancement, so the character would look like that:

Commoner 6 // Convoker 6 // Beastmaster 1

At the first level Beastmaster provides boost to your effective Druid level, so it will be a companion of 4 level Druid from the spot. I dont realy think you'll very much need any more levels in Beastmaster as it stacks with any companion advancing classes, and they have better class features.

From now on I see two options:

1. Take Druid for spellcastng, if you have room for it in your actions. Five levels will give you access to highest level spells even without that level lost due to Beastmaster. You also will have room for adding more prestige classes at those five levels later, as Druid is a regular class. Finaly, as a regular class, it has no prerequisites. It results in:

   Commoner 6 // Convoker 6 // Beastmaster 1/Druid 5

2. Stack some other prestige and maybe regular classes with nice class features wich progresses your animal companion. I'd consider Wild Plains Outrider, good class with quick advancement and ability to make a full attack after mount's single move. Two remaining levels may be of practically any class wich progresses your animal companion, probably those of a Beastmaster or even some regular class whose class features you like. It results in:

   Commoner 6 // Convoker 6 // Beastmaster 1/Wild Plains Outrider 3/xxx 2

I can't realy wrap my mind around Animal Ally feat mentioned by Chemus. I feel like, depending on your DM's judment, it may be quite usefull, but when to take it is a question I can't answer. Beastmaster and Wild Plains Outrider are both from Complete Adventurer.