When plants were invented, it's not as if The Great Creator assigned a proper spacing to each one. A "proper" spacing is determined by man in light of how useful he can make a plant be, in order to solve his needs. Therefore, it is the situation or yours and the site conditions that will guide one in determining an optimum spacing for the Hornbeam. Though you describe briefly some of the conditions, it's not clear how they exactly are, and a picture (that is not a close-up) will help those who cannot see it in real life, understand. We don't know what plant a "hedge row" is, so how the shade of the Hornbeam will affect it cannot be determined. Need that picture for more information.

not certain why others have reported that you should move your emerald green arbs. They should not spread to much into your fence since the fence will block some of the light and that side of the arbs will reduce their growth because of the decreased light. Also the 4 foot spacing apart gaps should not be a problem; especially if you plant a row of Frans Fontaine Hornbeam in front of the arbs. but stagger the Frans Fontaine row so that the planting hole centers for them in that row are centered and infront of the spacing between the planting hole centers of your Arbs The Frans Fontaine stay very narrow, in fact; by the time the Fastigia Hornbeams have lost their narrow shape and have begun to spread fairly wide, your Frons Fontaine Horbeams will still be remaining narrow enough to avoid making your screen planting appear overgrown. One other thing I am confused about is the advice given suggesting you could save money by planting wider spreading and faster growing trees and shrubs. Seems to me that would be a big mistake for your narrow strip of planting area, Such plantings would only serve to over grow your area and become an eyesore that would ultimately need to be removed. One other thing you should consider is the fact that your arbs are very easily killed by bagworms. Especially in zone 8 during the hot summer months when the arbs are slowing down a bit in growth just to maintain against the hotter and drier conditions. I usually do not like to use system bug killer products, but I have found that if I do not use the Bayer systemic bug killer product or some other systemic treatment that is just as effective. my Emerald Green Arbs do not survive, and they end up becoming a good feeding ground for the bagworms to over populate and start massively invading my dwarf Golden globes.

where are you ... many of us would NOT plant them in august .. depends where you are ... planting guide below ... [if location is above.. i missed it] imo ... planting for a sight block is a bit different than otherwise .. the faster you want the block.. the closer you plant them together ... its that simple .... you said: offer advice on proper pruning techniques and timing to ensure dense and faster growth again.. imo.. you do NOT prune to encourage growth ... first.. you need to thin in tree time.. which is counted in decades.. not a season or two ... trees have a root mass at lest twice what you see above .... a tree in a pot does not .... so .... with transplant of this size .... you spend two or three years growing a root mass .. and AFTER that .. then you start pruning ... think of every leaf as a food making machine .. so you do not want to be cutting off any of them.. during this time ... do you have any experience planting trees??? .. it is usually best done in dormancy ... when there will be little on no stress on those food making machines ... so /;.... in the meantime.. you hold over the plants.. until the proper planting time ... especially if significant root pruning is needed.. due to the large tree being in too small a pot for too long ... so the next trick is to water them properly in those pots ... and you do not water them like you would annuals and perennials .... those plants like constant available water.. trees dont ... again.. you have to work in tree time ... and you are not going to have your dream sight block in 2 years ... but done right ... you will be well on your way ... just keep that perspective in mind ... so..... spacing ... in my world.. warped as it is .... lol ... however far apart they have to be ... to fill the space with the number you have .... as i understand it.. when they grow together.. your not really interested in individually spaced specimens ... you want a wall or a curtain ... so who cares about it otherwise ... anyway .... you have a lot of issues to address.. other than spacing.. before you plant them ... if you wish .. we could discuss soil type.. drainage.... etc .... i dont know your experience level ... but it isnt as simple as just shoving them in the ground.. and hoping for the best ... btw.. if i planted 30 of anything.. i would expect losses ... so dont freak out.. if you lose one or two .. its just the odds of buying bargain stock in august ... you can make it work.. but dont worry about perfection ... good luck ... and dont forget tree time ... ken https://sites.google.com/site/tnarboretum/Home/planting-a-tree-or-shrub

Even one of those sweetgums (post immediately preceding this one) would not fit in the space discussed and still allow room to walk by. Otherwise there's a pyramidal European hornbeam in the county east of mine that could be 40' across, nearby the USDA station had a 'Frans Fontaine' hornbeam that was about 20' wide and so on. ("Had" because they cut it down recently, maybe because it was thought to have overwhelmed the planting site because it didn't stay skinny). Instead of columnar with branches coming low look for dwarf on a long single stem - from the perspective of your second picture all you need is a comparatively small bushy top at the level of the window. Dwarf hornbeam, dwarf crabapple, naturally small growing maple species - whatever you kind find. In either case (tall and narrow or lollipop/mushroom shaped) it's going to grow sideways over the neighbor's lot - so you need to be prepared for that. As in discussing it with them beforehand, so that you don't have an unpleasant surprise later - just as you are finally getting the coverage out of it you want (tree plantings take years to size up). A surprise as in one day you look at it and all of their side has been cut back to the fence - or even a couple feet back into your lot. (At my previous house a neighbor reached over a fence, cut a screening planting I had put in - that I thought they would appreciate being between them on their patio and my back windows - off at fence height apparently as far as they could reach into my lot. When I had occasion to discuss this unauthorized action with them later the complaint was the living screen was dropping dead leaves on their bark mulch).