Transplant, when used as a noun, can refer to either the object being transplanted or the act of transplanting itself. Transplantation, on the other hand, can only be used to refer to the act or the process of transplanting.
For example, you would say "the patient's body rejected the transplant," but would not say "the patient's body rejected the transplantation," because what is being rejected is the organ itself, not the act of medical surgery.
This difference in meaning comes from the suffix -ation, which means (according to Merriam-Webster):
the action or process of doing something
Aside from the rather intricate rules for what to do with the understood subjects of the second verb in these complex sentences, mentioned by Lawler in his comment, there is also a 3 way choice of complement type. What follows "consider" in the illustration you gave is taken to be a sentence, schematically [Lucas consider [Lucas bring back Hamill]], where the smaller sentence is called a sentential complement to the main verb "consider".
The 3 choices for complement type in English are that-clause, for-to, poss-ing. (I hope I didn't forget any.) (1) [Lucas consider [that Lucas will bring back Hamill]], (2) [Lucas consider [for Lucas to bring back Hamill]], (3) [Lucas consider [Lucas's bringing back Hamill]]. So part of what you're asking, I take it, is what principles determine for a given main verb ("consider" in the example) which of the three complement types will be possible, and what nuances of meaning will be expressed by the choice.
I'm sorry to have to report that the answer is unknown, and it may well be that there is no answer. English speakers may have to learn ad hoc for each complement-taking verb which complements are possible and how to interpret them. So for an English language learner, in this particular regard, grammatical study is probably not useful, and lots of experience with interpreting and speaking or writing English is all that can help.
The name of the relevant field of study, following Noam Chomsky in Aspects of the Theory of Syntax, is "the problem of verb subcategorization". It was tackled by George Lakoff in his dissertation Irregularity in Syntax, and there is a very good more recent discussion in McCawley's The Syntactic Phenomena of English.
Best Answer
If you aren't speaking legalese, and want to refer to the entire process of deciding on a contract,
If you just want to refer to the final stage,