Firstly you may as well buy a couple of boxes of cheaper lead ammo. You will get through them zeroing your rifle and becoming familiar with how it shoots. Putting a few dozen rounds through at 50-200 yards will be time well spent- especially if you try to replicate stalking conditions eg off sticks etc. Factory lead will be cheap.
Secondly- I'm not sure where you read that slow and heavy rounds are a viable option for lead free. Wherever it was- its wrong. 200m is quite far for lead free. Espeically on Sika. A heavy lead free bullet will not expand brilliantly at 200m. A light fast one will perform better. 200m is still quite far though.
Lead free needs to be FAST to work best. You get speed by keeping the weight low for the calibre. With a 270- this is probably around 110-120gr.
Finally- all factory lead free rounds work fairly well. The best ammo is the one that groups well in your rifle. Buy 2-3 different makes and try them at say 150 yards on a still day. See what groups best and then buy a few boxes. Anything that groups at 2" at 150 yards is more than good enough.
Not sure that lead free are a sub 200m only type bullet. Monolithic bullets work perfectly well out to well over 300 metres, and Sika deer really do not like them. Plenty of game is being taken with monolithics out to 500.
There are plenty of good options in 270. Fox, Barnes, RWS, Yewtree, Norma all produce good ammo that is well proven.
Lead bullets kill by fragmenting and send a shower of lead fragments through the animal. Depending on point of impact will depend on how quick they kill. Wound channel is typically much wider a couple of inches after entry. Given the fragmentation of the lead bullet typically 50% remains in one piece to provide an exit hole. If you are shooting bigger animals you need a bigger calibre / bigger bullet / lower velocity so the bullet stays together till it reaches the vitals.
By comparison modern monolithic bullets are designed so that on impact the front opens into a flower shape two to three times diameter, but the bullet remains in one piece.
The bullet cuts a round hole, like a hole saw right the way through the animal. Remaining in one piece, the bullet retains the energy and momentum to go right the way through the vitals. The flat shape of the flower provides a temporary cavity of perhaps 4 to 5 inches in diameter causing additional damage.
Putting such a bullet through the major arteries and central nervous system results in usual collapse on the spot and major loss of blood.
There is much less damage to meat, so much so that you can afford to shoot in line with the leg half way up. This results in taking out the aorta, top of the heart and major nerves in the shoulders, around the heart and into the spine. Animal quartering is not an issue either.
Frankly there are no real life issues with good monolithics. There are some that are less good and/ or designed for much tougher game than we shoot in the UK. The original Barnes being an example - very good on big antelope, whereas their TTSX is designed for deer.
Dont go heavy for calibre, you will tend to get better results with lighter bullets. So with 270, the 110gn bullets will be the length of a 130.
Some will shout about BC. Bullet density is just one factor, bullet length, shape and velocity are other just as, if not more important factors. A mono bullet will have a better BC than lead bullet of the same weight, due to its longer length.
Most mono bullets have driving bands and / or grooves, so there is surface area in contact with the bore of the rifle. This usually result in a higher velocity compared to traditional bullets of the same weight.
Prices of all ammo has gone up hugely, but there is not a lot of difference in price in ammo with a premium bullet whether it’s a mono, partition bonded etc.
If I was recommending one brand it would be the Fox. They are unfussy bullet that seems to work well in most rifles being a flat based cone point. Some would opine that the shape is not that sexy with a sleek ogive. Plenty of dead deer would disagree.
Monolithics are different to old lead bullets. They take a slightly different mindset, as many of old norms need rethinking. But most who have tried them won’t go back.