lead hardness

It makes a big difference. Too soft of a bullet for the velocity and it will not engage and lock into the rifling. The bullet will swage down to the lands diameter and fumble its way out of the barrel with no spin. Accuracy will be poor and keyholes likely. I have several recovered examples of this where a bullet is stretched out and no signs of rifling. Op are you using Standard lubed and gas checked or are you powder coating these bullets? When powder coating, I've been fine using straight clip on wheel weight lead ~11 bhn for 164gr bullets in both 300blk and 357 mag at 2,000 fps. You will probably be seeing higher velocity, I would start out with 14-16bhn for plain lubed lead.

Here are a few examples of bullets too soft for the velocity/pressure. Left is a 500mag bullet cast from 2/3 Clip on wheel weight and 1/3 pure soft lead. These were loaded with a minimum load of AA1680. You can see how wide the rifling marks are near the nose of the bullet but they settle down once the bullet gets most of the way in the bore. I solved this potential problem by using only clip on ww's ~11bhn.

The other two are 124gr 9mm bullets cast from 1/2 COWW and 1/2 pure soft lead. Loaded using HP-38, sized to .358 and fired from my beretta m9 with a .358 bore. Bullets just skidded their way down the bore. notice how the bullets are even more narrow/stretched out just below the truncated cone? no real signs of any rifling marks.

Hardness matters a lot.

I do not think you see much expansion on a 165 at 1600 fps. 18 is pretty hard even at the 1600.
If bone is hit first you may get some odd expansion or distortion of the bullet but more than likely it will poke a clean hole straight through. With any sort of cutting front edge to the bullet it could change things. I have killed a lot of deer with cast bullets. But will say any rounded nose and you have a problem. Put a cutting front edge to it and you get very good results. I have even used a 200 grain SWC in .45 ACP and it cuts a perfect round hole and bleeds them out right now. In the .357 mags I use a 158 grain SWC and it also cuts a perfect round hole and smashes bone in and out both sides and drops hogs right now. As you were already told if you get too soft it will end with bad accuracy and defeat your purpose. Cast bullets in rifles are usually not a very good choice for deer at any velocities they can be tossed. They make very good practice rounds. But, Deer have fell to .22 rim fires for many years.

I have been shooting the 165gr bullets from the Missouri Bullets Company which are a BHN of 18 with no leading to 1500 fps. Accuracy is good too

I looked up that bullet. It does have a flat front edge and looks as if it should do some cutting.
It may work fine for deer even at the speeds you ask about. I may have jumped on that too fats by assuming it had some sort of point. After seeing it, I have to say it looks fine to me. Should work. At 18 hardness I still am not sure about it doing much expanding but it may not need to. I guess I would go for it. If it ends up accurate it sure would be a sweet load as far as recoil.

For deer loads in the 30-30 I like a gas checked cast lead bullet of around 11 to 13 BHN sized to .311"at a velocity of 1600 to 1800 fps. which gives good expansion,basically that equates to air cooled wheel weights plus a bit of Tin.

It appears MO cast all their rifle bullets coated or not at the same 18 BHN which is not good for expansion even at higher velocity. A hunting bullet that hard depending on what it's alloyed with want be that malleable an may fracture and brake apart when striking thick bone. I've never tested any of there bullets on game or other test media si I don't know how they preform.

All is not lost as if no expansion is present the meplat or flat point of the bullet is what does the damage by creating the wound channel which is caused by the vaporizing or tissues which in deer as in humans is mostly water. This is known as Displacement Velocity or DV. The formula was devised by Veral Smith,using his formula which has never been disproven an can be found in his book Jacketed Performance with Cast Bullets. You can measure the meplat of any flat nose cast bullet and come up with a displacement velocity by using this formula Velocity times meplat width in thousandths of an inch, divided by 4. Ideal DV range for big game is 100 to 125, with 130 at the very max for fastest kills. At 100, wound diameter will average about 1 inch, at 125 it will be around 1 1/4 inch. The Lee 170 gr. FN runs around 105. Of course this is all relative depending on the alloy used an if it expands any or not,if the bullet is cast as a FN,HP or cup point and if the bullet were to strike bone.

Some other data from the Lyman #3 Cast Bullet Manual on hunting bullets using jacketed vs. cast loads at various BHN / Velocity.