I think you are going to have difficulty satisfying all of your requirements.

First, unless it's an annual, growing anything from seed tends to be a bit of a long term project - it just takes time for the plant to develop and mature to its ultimate size. Perennials will often take 2-3 years, trees and shrubs significantly longer. And you are going to be looking a lot harder for perennials that will achieve that size AND provide a year round privacy screen. If you do opt for a seed grown annual, look for giant purple millet. It grows rapidly to 5-6 feet, has a dramatic deep burgundy foliage and produces dense seedheads the birds will love. But it does die during winter.

I read your first post and understand the restrictions you face. However, you will get much better results and much faster if you can plant started plants rather than seeds. Is there an agency in your area that offers help to disabled homeowners? That may be the way to go. If so, you could plant pampas grass (Cortaderia selloana), an evergreen and very tall ornamental grass that requires very minimal attention once established. It can be planted from seed but you will be looking at several (3-5) years before it provides any kind of significant screening. And there is also the risk of substantial "crop failure" if you direct sow in the garden. Otherwise I'd consider some sort of upright evergreen shrub for your purpose - junipers, yews, etc.

I'd also not be overly concerned about your dogs and poisonous plants. Most plants have some toxicity to varying degrees, even some very common fruits and vegetables, but well-fed pets are seldom interested in grazing on them and in most cases they'd have to ingest quite a lot to produce any kind of reaction. Accidental poisonings of dogs and cats consuming outdoor toxic plants are really very rare.

What about Leyland Cypress? It's not so much an ornamental type grass or anything, but it is evergreen, is a great privacy screen, doesn't bloom or flower, grows fairly quickly and requires little maintenance. The only thing is that you wouldn't start it from seed.

I bought my parents a lot of them at the end of the summer season when they went on sale for little-to-nothing. If you didn't want to wait that long, you might be able to find some good deals in your area. My parent's have grown, tremendously, in the last 4 years, but wouldn't be tall enough to be a privacy screen the first year or so.