jwinterm recommended I take a look, but I only glanced at the white paper. Instead of changing chain work to motivate alternating, why not change the difficulty? It seems like this would reduce the number of orphans. Another idea for combining POS and POW is to let block wins be proportional to (% network HR) * (% network stake) but give a reward that's only proportional to the HR.
I'm more interested in new types of PoS (Casper, Dfinity) where the stake is at risk if there is a double spend. The ideal POW is to require all your miners to purchase equipment that is only useful for mining your coin and no other equipment can compete with it. It would also not use any electricity and it would not depreciate. This way the staked equipment / non-staked equipment ratio is a max. But instead of them actually possessing the equipment, you use a POS system that simulates the existence of the equipment. To do it correctly, the virtual equipment stake must be at risk as real equipment would be devalued if you attacked a coin too much and force devs to switch POW. Although I have not thought through the problem of old stakers giving away keys to old block wins.
Yes, LWMA with N=60 will vary +/- 20% many times a day as the link below shows for the coins I follow
http://wordsgalore.com/diff/N=144 will give it more stability. I have historically been biased towards faster response because response time is a function of N while stability is a function of SQRT(N), so you get more bang for your buck in a sense by keeping N low. But N=144 would certainly look more friendly and I think it will have enough speed in the vast majority of coins.
Edit: or LWMA with N=720. It would probably look good bit like your last simulation, as jwinterm said.
arto in the link above is using a 24 hour LWMA. It looks too smooth.
BTG is using N=45 and it looks just as stable as N=60, but it does have a lot higher hashrate than the others.
Wownero is going to use N=144 (1/2 day at their T=300
To clarify, I assume your POS block come in very regularly, otherwise I don't know how it has a difficulty algorithm like the POW blocks. Assuming that's the case, by "changing difficulty instead of chain work" I mean to drastically raise and lower difficulty for the POW block by a similar rule and leave POS as is. Your cumulative difficulty would then flow automatically from the difficulty.
you might really like what you find. 
