My thoughts and prayers go out to you during this difficult time. It is especially frustrating to see the path you want to take but feel unable to walk down it. The Church teaches that all marriages are presumed valid until proven otherwise. Marriage is a sacred covenant that was raised to a sacrament by Jesus because it is a mirror of His love for the Church. Marriage and family are the building blocks of society and the Church. If we weaken marriage then we weaken both society and the Church. Annulments are a judgment that no valid marriage existed because there was either a canonical impediment or one of the essential goods of marriage was missing from the beginning.
Let us remember that even in civil society where divorce is relatively easy to attain, it still costs thousands of dollars and is an intense process of splitting assets and assuming of debts/responsibilities. Civil law does this because it considers the marriage commitment to be important and thus requires its dissolution to be given intense attention.
In the same way the Church does not simply allow any one individual to decide for him/herself that a marriage was invalid. First and foremost the Church does this because Jesus Himself said that marriage was permanent until death (Mk 10:2-12; Lk 16:18). Secondly, marriage is a public action that has public consequences and thus the Church must be convinced that enough evidence exists that this important foundation of civil and religious society did not exist as was presumed.
As I have noted, the Church considers marriage to be of the utmost importance. When someone is entering the Catholic Church they must not be living lives that are explicitly in contradiction to her teachings. When someone is in an invalid marriage they are not committing only a personal/private sin but a public one as well. Public sin is not only a personal sin but a bad example to others. The Church cannot welcome into full communion someone who is publicly contradicting the teachings of the Church and, by example, encouraging others to do so as well.
It could well be that your previous marriages were invalid but there is insufficient evidence for the Tribunal to declare it as such. That is indeed a heavy cross to carry. I am unaware of the particulars of your situation by you may also want to discuss with your local priest whether the Pauline or Petrine Privileges would be appropriate to apply for in your situation.
I will keep you in my prayers and hope for a timely resolution to your problem.