Yes, we can. Estimates vary of the losses in long-distance HVDC (high-voltage direct current) transmission, but they're around 3-4% per 1000 km. Now, those operate at far higher voltages than you've mentioned: you wrote of 10 000 V, which is also written as 10 kV. HVDC runs at 100-800 kV, i.e. 10 to 80 times higher (100 000 to 800 000 V).
The idea of using a large-area transmission network to help average out both demand peaks and variations in supply goes back quite a few years: most notably to Gregor Czisch's thesis in the early noughties, which found that an international grid spanning Europe, the Middle-East and North Africa would enable 100% renewables with very high energy security, and would be about the same price as a fossil-fuel powered grid, without any of the pollution. (Gregor's thesis is available for free in German, and the English translation can be bought as a book from the IET. It's an academic thesis, so it's a very dense read).
Since then, a lot of work has been done on these: they became called supergrids, and various people (including me) looked at scenarios built around supergrids. Some of the interest has waned now, partly because a lot of people just take it for granted that that's the obvious way to do things, and that more and more HVDC transmission and other international electricity connectors are getting built. If you're interested in more about the USA case, see the Tres Amigas Superstation, also work by Mark Z. Jacobson & Mark Delucchi, and work by Chris Clack and Alexander (Sandy) MacDonald.
Peak hours vary by country: in the UK, the biggest peaks are winter evenings around 17.30, with a smaller peak in the morning. In Germany, the demand curve tends to peak during the middle of the day. So a wide-area grid with high-capacity long-distance transmission helps there: it's not just an issue of spanning timezones, but also spanning different economies with different rhythms; and spanning different climatic zones, so different requirements for heating, ventilation and air-conditioning, which follow different diurnal and seasonal patterns.
And additionally, weather systems tend to be at most about 2000 km across, so having a grid that is larger than that, means that it will never be dominated by a single weather system; meaning that wave, solar, wind and hydro will all get smoothed over that whole area.
High-capacity long-distance transmission networks aren't a silver bullet: they don't guarantee energy security. No one thing does. What they do do, is take us a long way along the path of energy security, at low cost relative to the alternatives.