There's no contradiction between paper ballots and speed. In my country we all vote with paper ballots, then at the closing of the polling stations the members of each voting table punch the results of their urn into a laptop which connects to the electoral authority. In 3-4h max the elections results are out.
For security however, after punching the numbers into the laptop, ballots are re-sealed into the urn and physically sent to the electoral authority, where in the following days public officers count them manually again. There has never been any meaningful deviation detected to date.
This way, you have the security of paper ballots (they are on sight of party volunteers at all times) with the speed of electronic vote aggregation.
Are you Mexican? Our system is the same, but a critical factor helps it. Every citizen has a voting credential, and every booth has a list of voters. You can't vote without your id, and while you can vote in secret, you can only vote in your designated booth.
This gives the system its agility. Our recent presidential election had a reliable statistical advance (PREP) at 23:00 the same day, and the next day every single vote of every remote booth was fully accounted, and the result confirmed the PREP.
The Mexican electoral system is surprisingly effective, yet we have the same core problem of democracy: we need better candidates and less gullible voters :/
This thread [1] on /r/Mexico made me think that voting credentials don't work very well. I haven't read any technical analysis of the system, but everyone in the thread is talking about how easy it is to vote multiple times.
For security however, after punching the numbers into the laptop, ballots are re-sealed into the urn and physically sent to the electoral authority, where in the following days public officers count them manually again. There has never been any meaningful deviation detected to date.
This way, you have the security of paper ballots (they are on sight of party volunteers at all times) with the speed of electronic vote aggregation.