And it was evening, and it was morning; the third day. Ha ha.

Someone brings her breakfast and notifies her that the supplies to build a printing press have been assembled in a workshop downstairs and she can be brought there as soon as she's ready. 

She will eat very quickly and be ready as fast as she can!

The workshop has a forge and more iron and wood than she'd plausibly need. "We have people who are fairly good at ironworking if you're able to delegate anything. I also sketched out the forms for each letter in our alphabet."

"Let me see...oh, including the vowels shouldn't be too hard at all, we can just have thinner slots over each of the regular-sized slots and blank pieces that go there when there's no vowel."

"And below for some of the vowels, written Sindarin would generally look like this." He starts writing. "With the different letter heights it seems like it'd be difficult."

"If we're willing to leave enough space for the differences...It probably won't be as elegant as the handwritten version, at least not on the first try, but it would probably be legible. Alternately we could have different pieces for every possible vowel-consonant combination but that seems tedious."

"There are only five vowels and sixteen consonants, so not too tedious if you think it's worth it."

"I'm strongly prioritizing readability over elegance; you seem like you might value elegance more highly in this situation and I think individual blocks might be the best way to achieve elegance, or at least the best way I'm going to think of in the next five minutes."

"Then let's do them. I can't see the press being widely adopted if it makes the language look kludgy or ugly."

"Once the basic principles have been established there are probably people who can take more than five minutes to think of better alternatives, but by all means let's go with the best idea we have right now."

"All right. I can ask someone to design the letter tiles, that seems straightforward enough that anyone can do it. What about the press itself, is that complicated?"

"Not all that complicated, really," she says, and then launches into an explanation of how printing presses work and are put together.

Which he follows and is happy to assist with.

Then at the end of this they will have a functioning printing press! Theoretically functioning. It doesn't have any letter-pieces yet.

Some other people have been called in to help with the letter-pieces, and are pouring molds for them while the press itself is assembled.

When that's done Illia can cool them quickly enough that they can test the press sooner rather than later.

They have the whole thing working and are assembling letters to test with it by the time someone brings lunch.

Ooh, lunch. It's a good thing her part in the construction is done so she isn't too distracted to eat.

"Care to start dictating the instructions so I can write them? I'm happy to teach you how to write in our alphabet as well, but it doesn't seem like a priority."

"Yeah--I do want to learn to read, I dislike the idea of being illiterate, but it's not an immediate priority." And she starts reciting some of the lessons she'd drawn up in her head as she fell asleep last night and while they were working.

He writes them swiftly and neatly and stacks them up for the testers to assemble on the press. "Can you put your hair up again, Illia?"

"Um--okay, why?"

"It's really unconventional to wear your hair down, it's - similar to the Mannish taboos around nudity? I don't know if your nation has those."

"...Yes. We do. We really do. Are you telling me I metaphorically had dinner with a King naked? Couldn't you have told me this sooner?" She looks utterly mortified.