I also like the look of a cottage garden, and I always plant things closer than the label says, so sometimes end up moving them.
(Plus I never believe that they are going to get as big as they do!)
Not knowing which plants you're talking about is hard to say, but - I've never lost anything to transplant. When I move something I always keep it well-watered til it sets in, about a week, and if the sun is very hot, I shield it from the sun.

Generally speaking, something with a long tap root would be harder to transplant, but by no means impossible.

I planted chinese houses about 8" apart this morning and persian catmint about 4-6". My poppies are all about 6" apart.

They're just so itty bitty right now putting things further apart than 8" seems ridiculous. I know they'll grow, but I'm not quite sure I entirely believe it.

I plant them close--some within 4-5 inches of each other--and let them fight it out. The beds are still so empty there's plenty of room but I don't want paths between the plants, I want plants cheek-by-jowl and growing into each other. If a combination doesn't please me, I'll change it but until I see it when the plants are mature, I leave it be. I know I made some mistakes last year planting short perennials behind tall ones but that's part of the fun--learning about them and getting familiar with when they bloom, how tall they get and what others look good growing near them.

If I end up with a mashed up mess of overcrowded plants, can I move them later?

Move stuff around to your heart's content. Some perennials will sulk if you move them and most will suffer at least a setback if they're moved during hot, dry weather. Try to move things when it's going to rain and be sure to fill the hole with water (and let it drain) when you plant. Shade the transplants from hot sun with a lawn chair or umbrella for several days while they adjust to their new home. ellenrr is right about plants with deep taproots but there aren't a whole lot of those that I know of.

Closer spacing, less weeds is my motto! I have developed my gardens through WSing and find this close spacing comes naturally when I have way too many seedlings and not enough ready real estate. Also the HOS method brings nice full bunches of plants - I try to do at least 7,9 or more hunks in a circle/oval grouping. I do plan a "working the garden" path (most are slates) so that I can get to things to cut flowers or tidy up. I found it really frustrating when I had deep beds that were so full, there wasn't a way to get through the jungle.

For me the trickiest thing is planting perennial seedlings. Many times they stay small and dont bloom the first year, then become giants the next. I always have to transplant them. Last year I put in a little side bed in the back that is just a holding bed for 1st year perennial seedlings. When I transplant them this year I will be able to place them where they make sense.

The logical thing to do would be to look up the spacing of the plants, and adjust accordingly. "Space plants 12-16 inches apart." Make them a little tighter than that-perhaps 8-12.

Most perennials I know of should be divided every 3 years-if you make them too tight then perhaps in 2 years instead of 3 you would need to divide? If they are handled too much, will they die? Most likely not, just do it in early morning, or late evening, when the sun is least harsh, water thoroughly when done. General rule of thumb is to divide spring flowering plants in the fall, and fall flowering plants in the spring (opposite their blooming time so the plant can put its energy into flowering when needed, instead of recovery from transplanting). I love the idea of shading them with a chair or umbrella.

My philosophy is I'd rather see them full NOW and divide later. Take the chance, keep them tight, and move them in the fall/spring if they look overcrowded.

What about delphinium? Are they one of those perennials that will stay small in their first year? I wanted to put in a bunch of Pacific Giants, but I can inter-plant with larkspur this year if the delphinium are going to stay little.