Ahh, Chase scenarios; those are often tricky. If you have any experience with 4th Edition though, they become less so. True, that 4th edition and 5th edition rules and dynamics are quite different, but there is much that can be sampled and converted.
On page 252 of the 5E DMG (Dungeon Master Guide) you will find the rules on 'Chases' , and this leaves much to be desired as you found out while attempting to use them for your graveyard chase. The roll tables are neat, until you realize they can not apply to every scenario, or environment.
There is nothing else that is 5E SPECIFIC that I can offer you, except my 5E conversion of the 'Non Combat Encounter' system from 4E. So what do you do? You pick an instance or 2 for failure. The party get's too far behind the Githyanki, or the Githyanki reach their objective. Then you create hazards your party might face while chasing down Gith on a moving train with several carts to it. The most important part of it, is to make a list of possible important skill checks and then have the party pick from that list for them to focus on through the course of the chase (how many they pick is dependent upon what the CR of the Chase Encounter is), and they roll those skill checks and the dice decides if they pass or fail.
You notice a Githyanki is attempting to cast Misty Step! (Arcana check to see if anyone proficient in the skill notices) If the roll is higher than a proper DC for their level , they notice and can attempt to counter spell or otherwise stop the Gith from teleporting.
The Githyanki begin to sprint ahead of you! (Atheltics check to see if members of the party can keep up with them) If they fail the check, the party falls behind 1 level, if they succeed then the Athletic member keeps up and leads the party ahead.
A Githyanki launches a Firebolt at you! (Acrobatics check to see if you evade the cantrip.) You can also use random acrobatics checks for them jumping from train car to train car.
These are just a few 'chase situations' that you can apply a Skill Check to and have the party try and get past it by choosing who's the best at each skill and dividing the checks among the party. The best thing about the 'Non Combat Encounter' mechanic is that you can assign exp to these like normal encounters even though they are not engaging in combat where they kill things.+