The problem with too much [uninformed] prayer-chopping is that a lot of the siddur was consciously designed to invoke certain emotional responses, and mental committments.
Extreme Godol Hador blogged on the The Problem with Davening, about the inability to express kavvanah while rattling off the prayers enroute to work.
I taught a shiur on the siddur one summer. We didn't get beyond the last Hallelukah, but we did cover a lot of the intentions. On the basis of that (largely based on R' Schwab's book On Prayer), as well as some tefillah columns I wrote for AishDas (based on the shiur, and other materials such as Otzar Hatefillos, "My People's Prayer Book" and even Art Green), I disagree with some of your proposed cuts, and might offer others.
First off, korbanot, as well as Rabbi Ishmael, are only there to provide a "minimal Torah study", and by rights should come right after the Birchot haTorah. The siddur has a lot of such things, as different people added what they thought ought to be "minimal torah study", so we have three sections trying to do the same thing. You should be fine with the brief bits from Torah (birchat kohanim), Mishnah (things with no measure) and Gemara (things whose reward continues in the next world).
Korbanot through Rabbi Ishmael is one addition (although you ought to say Rabbi Ishmael in a minyan to trigger Rabbunenkaddesh for the mourners; aggadita, not halacha, triggers a Rabbi’s Kaddish [according to my rav, R’ Moshe Sokol]). Pitum haketoret through H’ mevarech et amo bashalom is a third attempt to shove Torah study into davening; again, it should be said by a minyan to trigger Kaddish deRabbanan for mourners, although without mourners, I’d say it could be left out.
Second – morning brachot. I’d do the opposite of what you do: leave in the Shelo asanis (if they really bother you, there are Gemara-based positive formulations for one or two of them), since they’re based on our obligation in mitzvoth, while leaving out all the other ones. According to the Gemara (a Braisa on 60b?), they should be said as one wakes up in the morning: hanatan lasechvi binah for hearing the alarm clock, pokeiach ivrim for opening the eyes, matir assurim for disentangling from the sheets, zokeif kefufim for stretching, etc. Without the context of the actions in waking up, they become empty and meaningless.
Leolam yehei – yes, leave that in, it’s pivotal to regaining consciousness of being in the world. Although, when I’m in a hurry, I do often leave it out. It’s not strictly speaking a prayer, rather, a meditation one should make on a daily basis; by adding the introduction “One should always say upon arising”, it becomes yet another attempt to sneak in some torah study.
The balance aspect of the meditation is key – as one Mussar great has said, one should keep two pieces of paper in his pocket and check them now and again. One says “the world was created for me”, while the other says “I am dust and ashes”. This section makes us conscious of the balance – we are all nothing before God, but still God chose us and loves us. Therefore, from that balanced position, we testify to God’s existence and unity twice a day, and thus sanctify His Name.
Note that the brachot section is left out in many shuls, they begin at Rabbi Ishmael or even Baruch Sheamar (not every shul says the early kaddeishim). It’s expected that one has said them at home.
The brachot have a progression:
- Body: asher yatzar, al netilat yadayim.
- Soul: elokai neshama
- Mind: Torah brachot, mitzvah brachot
- [Interjection of what should have been done earlier: other morning brachot]
- Relationship to people: hamachazir sheinah.
- Relationship to God and self-balance: leolam yehei
- [Torah study: scripture – korbanot, mishna- eizehu meqoman, gemara – Rabbi Ishmael]
I’ll discuss pesukei dezimra next.
But these simple kavanot, intentions, might help in one's davening. Kavvanah need not be highly complex kabbalistic structures - that's a late (16th-century) invention.