The main issue at hand, relevant specifically to a hachnasat sefer Torah for a new sefer Torah,[2] is the permissibility of writing the sefer Torah’s final letters, as the minhag is to do so on the day of the ceremony.
The mishna[3] states that it is forbidden to write even a small part of a book, including holy scrolls, on Chol HaMo’ed. The Rama[4] cites two opinions as to whether this is permitted if the masses need the book after the chag, and he concludes that it is permitted if one uses simple, “non-artisan” writing. In other words, according to the lenient opinion, the mishna refers specifically to cases in which there is no acute need to write on Chol HaMo’ed itself. These halachot follow the rule that simple work (ma’aseh hedyot) is permitted on Chol HaMo’ed for festival needs or for communal needs that are sufficiently significant, even if they are only for after the chag.[5]
Since writing a sefer Torah certainly requires an expert acting carefully (ma’aseh uman), it should be forbidden on Chol HaMo’ed. The Shulchan Aruch[6] does rule that if there is no other sefer Torah for the community’s Torah reading, a sefer Torah may be finished on Chol HaMo’ed for that purpose. However, it does not sound like that is your predicament.
Despite the above, there has long been a phenomenon of hachnasot sefer Torah held on Chol HaMo’ed. Some poskim[7] criticize the practice. However, several poskim justify the practice when it is performed in a particular – and anyway common – fashion, as we will now discuss.
Usually, the main writing of the sefer Torah is completed days before the event, except for the last letters, which are written at the hachnasat sefer Torah itself by the sefer’s owner and his honorees. To facilitate this, the sofer uses one of two systems: 1) He writes the letters in very light ink, so that the donor/honorees write on top to darken them. 2) He writes “hollow letters” and has the donor/honorees fill them in. Some poskim suggest that in these cases, the halachic writing already exists, in which case the writing that is left for the end does not constitute a melacha.[8] Moreover, even if this is a full melacha of writing, it is an example of ma’aseh hedyot, as even a non-expert can follow the tracing or fill in the hollow letters, and in such a case, writing is permitted even for a simple mitzva of an individual or for an enhancement of the chag.
What mitzva or enhancement of the chag applies here? Some say[9] it is the mitzva of having a sefer Torah. Although some of the leniencies of Chol HaMo’ed apply only if one had to do the work at that time (a condition that might not apply in your case), festival and mitzva needs can be done even if they could have been done at other times. Some question[10] whether the writing of the sefer Torah is considered a mitzva in our days, but the argument that it is not a mitzva seems weak. In any case, since the whole celebration is such a joyous and chag-appropriate activity, all of its standard elements, which customarily include writing the last letters, are festival needs. (The poskim are not concerned with the possibility that the celebration might impinge on the proper focus on the chag, which is the reason that weddings are forbidden on Chol HaMo’ed.[11] A Torah celebration of this type is within the appropriate focus.) If the sefer Torah will be read from during the chag, including Simchat Torah, that should also be considered a mitzva purpose.
Thus, under the above conditions, a hachnasat sefer Torah is permitted according to most poskim, including the Beit Yitzchak,[12] Kaf HaChayim,[13] and the contemporary Chol HaMo’ed K’Hilchato.[14] As mentioned, there is also some history of leniency. Some poskim[15] are willing to be lenient only in the case of real need, which you indicate you have.
In summary, if it will be most appropriate for the celebration to take place on Chol HaMo’ed, feel free to do it then. Make sure the sofer completes his part before Yom Tov and leaves any expert brush-up work for after the chag. Mazal tov!