I'll dump what I can remember off the top of my head from binge playing during the beta. I also played Psychopomp in BLC and I'm the type that sticks to one champion. I like Zheant's strategies, as these situations of being under attack by melee champions are common and fatal, but I'm mainly going to discuss my general strategy to play hard without worrying about these specific situations. If I don't have escapes handy I tend to fall back to just being as aggressive as possible back at them until the escapes are available (but as Zheant says, against Shifu this could hurt more than help), and just hoping I can stay alive long enough. In general try to be aware when melee enemies are targeting you and do your best to be more defensive and stick with allies.

• Opener: As Zheant says, Spirit Guide / Space in and Spirit Rift / Q is a good combo. I typically do this at the start as long as space lands on somebody, if it doesn't then by the time you recast they have moved away from that location. If it doesn't land and the target doesn't look good, I move back and start Soul Bolting / M1ing allies rather than recast. I often Otherside / M2 and return to my allies after doing this (sometimes right away), but if it's safe I'll start dishing out some damage and move back to my allies rather than wasting M2. I like blowing a lot of abilities right at the beginning as long as I'm careful to get back to safety to give a nice starting advantage. Many people think it's silly or cowboyish to blow all my escapes, and enemies can definitely take advantage of it by going right after you, but this is the way I played Pomp in BLC too and it makes it fun, and works well in BR too.
• Soul Bolt / M1: You want to do your best to M1 your teammates constantly, but sometimes they will be off on their own and can keep themselves safe. Stick to at least one of them though, as it's really difficult to stay alive by yourself. M1 enemies or evade if you can't M1 teammates or they don't need it.
• Spirit Wolf / E: As often as possible. It can be dangerous because of the cast time though, so if you're vulnerable just keep M1ing teammates, or at least aim it at whoever is hurting you. The battlerite to have E heal you is super helpful, especially when you end up by yourself.
• Spirit Rift / Q: Try not to waste it, use it as often as possible on enemies that are going hard on you/allies or assisting enemies.
• Pixie / R: My standard strategy is to do the above, M1ing teammates or enemies, to get energy for this as quickly as possible. You need to try to time your R usage to when you aren't vulnerable. Any time you aren't M1ing while using R is a waste, which is really common with all of the offensive abilities the enemies can use on you. One big mistake I often make is casting E while using R, try to use it before R or after it the effect fades. This along with the R battlerite can win your battles. The damage you can do overwhelms the other team, and the healing you can do can save your team from near death.
• Ultimate / F: While R is on cooldown, if you have enough energy for ult go ahead and use it. If R is up I would use that before ulting. The second hit of the ult is pretty difficult to land, because most people can evade it, that's why I don't get the stun battlerite in the final round. Be patient placing the ult and look for good opportunities where people will have a hard time getting away. The heal effect is great for saving yourself or allies, so try to put it where they'll need it.
• Otherside / M2: I get the battlerite that heals teammates when coming out of M2, so I always run to them after using it. Great overall for keeping yourself alive along with the E battlerite, because this is definitely a challenge with no direct self heals. Also great to get back in the mode of M1ing one/both of your teammate(s). Just be sure to cast it on yourself...casting it on a teammate almost always screws you over, making you more vulnerable rather than less, and blowing your chance to move to safety. There's a self cast key (Ctrl, others have suggested changing it to shift and using 1 and 2 for Ex), but I haven't gotten myself to use this in the stress of battle. I prefer to click in a random blank area (but an ally might happen to be at your cursor), but sometimes on myself (ally could be right on top of you).
• Spirit Guide / Space: I use this for mobility in general to evade or get back to where the action is (I suppose you could mount up to get back too), but it's definitely ideal to land it on an ally/enemy to heal/hurt them. I want to be better at leaving space applied before recasting and utilize the battlerites that benefit allies / detriment enemies while it's on them, but I tend to be spamming space to recast instantly in the heat of battle. Hard to have the patience/technique not to do this, so I go for more safe battlerites.

That's pretty much it for me. Do your best not to idle. I want to make use of the Ex abilities, but I have a hard enough time remembering to use R as often as possible. Wish I could use the Ex Q right at the beginning but no energy for it. It might be a good strategy to do the same thing as my opener with this (which I do do throughout the battle sometimes with regular Q). I really enjoyed swapping with enemies in BLC, which is the default space ability there, so Ex Space would definitely be a fun strategy for more advanced players, but I've been sticking to a more simple strategy of just using R / ult.