Will (or "do") people in heaven get to interact with Jesus, independent of massive crowds?

A few verses:

Jesus personally eats with His disciples:

Matthew 26:29 But I say unto you, I will not drink henceforth of this fruit of the vine, until that day when I drink it new with you in my Father's kingdom.

Notice the way Jesus interacts with the people:

Revelation 3:12 Him that overcometh will I make a pillar in the temple of my God, and he shall go no more out: and I will write upon him the name of my God, and the name of the city of my God, which is new Jerusalem, which cometh down out of heaven from my God: and I will write upon him my new name.

"I will make...", "I will write..." - Jesus personally does these things

Revelation 3:21 To him that overcometh will I grant to sit with me in my throne, even as I also overcame, and am set down with my Father in his throne.

You can see the personal care given by Jesus to the redeemed:

Revelation 7:17 For the Lamb which is in the midst of the throne shall feed them, and shall lead them unto living fountains of waters: and God shall wipe away all tears from their eyes.

The imagery of the good Shepherd is used here. The lamb shall feed them.

Then there is a special group: Speaking about the hundred and forty four thousand, the Bible says:

Revelation 14:4 These are they which were not defiled with women; for they are virgins. These are they which follow the Lamb whithersoever he goeth. These were redeemed from among men, being the firstfruits unto God and to the Lamb.

In Jesus's own words:

Luke 12:37 Blessed are those servants, whom the lord when he cometh shall find watching: verily I say unto you, that he shall gird himself, and make them to sit down to meat, and will come forth and serve them.

The basis and inspiration for this answer is a great book named Beautiful Outlaw by John Eldredge. This book delves into the personality of Jesus by taking well-known stories in the Gospels and bringing them to life. We tend to think of Jesus as being too Holy for us, when in fact people flocked to Him and He was the most human man ever (He was fully God and fully man, and emptied Himself of His divinity).

Jesus was just as human as the rest of us. He dealt with our temptations, He cried, He got lonely, He felt the need to be by Himself after the death of His cousin, He got angry, He was joyful, He was playful, He was capable of surprise, and He took shortcuts.

Crowds flocked to Jesus wherever He went, to the point that even going across a lake didn't keep them back. People with disabilities were constantly seeking Him out and going to Him for healing, like the two blind men that called out, the woman who had been bleeding internally for twelve years, and the blind and lame immediately after Jesus clears the temple. The guy that denied Jesus three times (and then had Jesus look straight at him) was the same guy that put on his clothes, jumped into the water, and swam at least a mile to shore to Jesus. Jesus was also willing to get up in the middle of the night to talk to a true seeker.

Jesus was extravagantly generous (what else do you call 605-908 bottles of the best wine?) and loved everyone equally (even the children!). Jesus was also quite personal and intimate and will personal and intimate be in Heaven as well (the white stone engraved with a name that only two people know).

While we don't know how many people will get to heaven, it seems that it will certainly be "a lot" -- far more than could reasonably expect to talk to Christ on a regular basis, for example. And I imagine that the Son of God probably will be (or "is") quite busy with very important matters.

So, will (or "do") individuals in heaven have an opportunity to interact with Jesus? Is there some equivalent of going fishing with Christ? Or will he be like a celebrity who, under normal circumstances, maintains a certain distance? Will there be something like "town hall meetings," where he stops by different parts of heaven every so often and talks with the local residents? Will those who lived more righteous lives and so "stored up more treasure in heaven" have preferential access to God's time? Or is there some other alternative?

First off, Jesus is God. If He wants to talk with multiple people in person simultaneously, nothing's stopping Him. Also, given what I've pointed out, there's NO WAY that Jesus would let "very important matters" keep Him from interacting with the people He loved (and loves) SO MUCH that He died for them. I don't see why Jesus wouldn't go fishing with someone who loved fishing, and He definitely wouldn't be distant like a celebrity. Nor would He spend more time with people who had been believers longer (cue this parable about vineyard workers). Ha, if anything, He'd spend more time with those who weren't believers all their lives! (Finding that one lost sheep was cause enough for great joy.)

Finally, Jesus Himself is preparing a room for us and we'll get to live there for eternity!

According to the christian soterology, not only in heaven you can interact with Christ, but also here, on earth. We know from the lifes of saint Silvan of Athos or saint Seraphim of Sarov that they have seen Christ himself.

Of course there are people who believe that this form of interaction isn't a real interaction with God. It is only some created thing that we can see from the God's will. This view was however condemned by saint Gregory Palamas. So this is at least what Orthodox Christians firmly believe. If you are not Orthodox, you may not accept it.

On the other hand - if we are unable to interact with Christ in heaven, then what kind of heaven it would be? Why would it be desireable for us? Imagining heaven as full of bodily pleasures is rather muslim thing not christian. For a christian the main goal is always Christ and his love.

Two quotations from Bible to support the idea:

And Jesus said unto him, Verily I say unto thee, To day shalt thou be with me in paradise (Luke 23, 43)

For I am in a strait betwixt two, having a desire to depart, and to be with Christ; which is far better (Philippians 1, 23)