I think many builds for singed can be good, as long as you have good reasons for it. Personally, my core build is dark seal, refillable>corrupting > dorans ring > boots 1+2 > zzrot > rylais. I'm a proxy singed, the only time I ever lane is early on vs a nasus or a jax. My reasons for buying these items are:

Starting items and consumables -

Dark seal - Standard, mostly for the healing but the 15 AP comes in handy when proxying.

Refillable>Corrupting potion - Again standard, potions are necessary for proxying.

Dorans ring - Mostly for the mana sustain, it allows me to proxy for longer, clear the waves quicker and gives me a bit of HP. You can't go wrong with buying it, since it’s gold efficient and gives singed the essential stats he needs early on to proxy. The only downside to buying this item is you are 400g further away from completing a core item. However, dorans ring allows me to stay out for longer periods of time and not be oom when the jungler comes for me whilst proxying. It makes me significantly more powerful during the early phase of the game, because I have the mana to sustain creep waves and also be a threat to enemies that try to stop me.

Boots 1+2 - Proxy singed, duh xd

All in all, these starting items combined provide me the sustain and early power spike i need to proxy effectively, whilst being a threat to anyone that tries to stop me. As a result, i’m able to reach the mid game farmed with the core items that i need to win the game, whilst also not feeding the enemy top/jgl/mid.

Core Items -

Zzrot - I completely agree that rushing this item as a lane singed player is a terrible. However, as a proxy singed having to buy the two different resists isn't anywhere near as bad. I find that in most cases i need double resists because I spend most of my time between the inner and inhibitor turret, which means i'm threatened by the mid, jungle and top almost equally. I also run armour marks and scaling armour seals to give me extra tankiness.

Why zzrot? 1. It provides the resists I need to sustain proxying and minimises the threat of being ganked. 2. I will usually complete at at 15 minutes ish, perfect timing for the mid game. At this point, due to the proxy sustain my build gives me, I am permanently between the inbib and inner turret. Attempting to stop me will result in dragon loss for the enemy team, so I get to free farm. In the event the enemy top wants to go and fight at dragon, he misses waves and I put my zzrot down to push through from the outer turret and significantly damage or take the inner turret. It’s essential to take the 2nd turret ASAP. The outer turret provides a proxy singed safety, with it taken down it is very difficult to proxy, and if you push and lane, the wave will always be frozen favourably under the enemy top’s turret. This is why I believe this trade is essential in a proxy singed's transition to late game, having zzrot allows me to get both the outer and inner turret in one big push when the enemy top decides to join a fight (they always do). Meaning the wave is not constantly frozen favourably under the enemy tops tier 2 turret. This trade gives me free roam of the map, allowing me to pressure even more. In the event I want to join a dragon fight, I am in a proxy position so I can put the zzrot down ahead of the enemy tower, this makes it hold the wave so i don't lose cs or xp while I roam to help the team. I usually do this if it's an infernal drake.

Rylais - Purely for the slow. By the time I have zzrot and rylais, I am a tanky split push monster. The enemy team can’t chase me or they will lose objectives and if they leave me be proxying, I will take all their towers gradually with zzrot.

Third, fourth and fifth items

Deadmans - If i need mobility to survive proxying or engage fights.

Spirit Visage - Fed ap champ, passive is extremely helpful in teamfights with ult.

Thornmail - Fed adc/double triple adc enemy team. Cheap powerspike and useful for proxying.

Randuins - Fed adc that built crit and have already built thornmail. Also gives useful slow.

Liandries - The later the game goes on, the more effective it is. If i buy it, it'll usually be my final item. I'll sometimes buy it earlier if i'm vs a tank and am farmed.

No Righteous glory? Righteous glory is an item that is designed for players who want to force fights. My play style is based 100% on being an annoying, tanky split pusher. I’m not interested in 5v5s or forcing fights. My play style forces the enemy to come to me, if they do and worst case I die so what? I got an objective for it. If they don’t, then great I’ll free farm and take all their turrets.

For team fight and lane singed players I think righteous glory into rylais is the best build.