The planting by the mailbox looks fine to me as it is now.

Certainly, privacy is nice but the sheer number of tall bushes crammed into that space is what is making the yard look a little unkempt, in my opinion. I would get rid of the three dying bushes on the side. I think they detract from the nice arrangement by the mailbox.

This is how I would approach this. Before you stark hacking at bushes, mulch the whole area into an island with dark, lovely mulch. This will instantly make everything look better. Whatever is dead, take out. Assess area from street and house. Stop or continue. Is something straggly or overgrown? Take it out. Reassess again. Ask yourself if you comfort zone for privacy alarm is going off! If not and you are not happy, take out more. Replant each time with low shrubs' hosta, bleeding heart and other shade loving perennials. Annuals like coleus can add a punch of color until the first frost.

Try a white picket fence. It will immediately up curb appeal.

I would call a certified arborist and have them assess your shrubs and trees. Judicious pruning of the trees can open up the canopy and permit lower level shrubs and plants to thrive. At the same time, you can trim many of the shrubs yourself. The privet bushes beneath your mailbox can do with vigorous reshaping. If you don't like the lambs ears, remove them or transplant them. Yes to a nice top dressing of mulch! Your Bradford Pear, while lovely, has a limited life expectancy; they tend to split in windy conditions. You might think about a long term replacement for it. Good luck!

I completely agree with ptreckel, keep the tree but have someone come out and prune to open up the canopy a bit. No one else mentioned this, get rid of the IVY asap! It will take over the tree, surrounding shrubs, and planting beds. We had a similar issue and it was a bear. Here's what you need to do... or have someone else do :)

http://treestewards.org/take-ivy-off-trees/

For a contrary view, I offer the following.

If you had suffered heavy snowfalls, your fine tree would have split apart already. It is dying, as you admit. It is shading all the plants beneath it, as you tell us. It is also soaking up the moisture and minerals from the soil, thus depriving its neighbors of sustenance. It will only grow more dead, while you improve the planting beneath it with shade plants.
Have the tree removed and the stump cut down to 12" or more below grade, so the groundcovers can spread over its grave. Farewell, sweet pear, you have served us well.

Improve the soil throughout,and add groundcovers and/or sod to cover the open bed.
Continue the hedge to enclose the bed along the street and drive entrance, with no pruning for two years to see how it all fills out in the renewed sun and fertilization. Perhaps that has helped bring you from "that house" to "That Great Warm House of friends" during the two years of growth.

Move the lamb's ear to where you can enjoy it, while sitting on your front terrace, having coffee with your neighbor.

Just my two cents, but your cottage is adorable. Currently it's hidden behind so much stuff it can't be appreciated from the street. Be willing to open up the front yard a bit, even at the sacrifice of some privacy. Don't hide your home's light under a bushel (or bushes, in this case)!