Can I use Squid to upgrade client TLS connections?

I'm trying to allow legacy systems (CentOS 5.x) to continue making connections to services which will shortly allow only TLS v1.1 or TLS v1.2 connections (Salesforce, various payment gateways, etc.)

I have installed Squid 3.5 on a Centos 7 server in a docker container, and am trying to configure squid to bump the SSL connections. My thought was that since squid acts as a MITM and opens one connection to the client and one to the target server that it would negotiate a TLS 1.2 connection to the target, while the client was connecting with SSLv3 or TLS 1.0.

Am I totally off-base here, or is this something that should be possible? If Squid can't do this, are there other proxies which can?

My current squid configuration looks like this:

access_log      /var/log/squid/access.log
cache_log       /var/log/squid/cache.log

cache_store_log none
cache           deny all

http_access     allow all
http_port       3128 ssl-bump cert=/etc/squid/ssl_cert/myCA.pem generate-host-certificates=on version=1

ssl_bump        stare all
ssl_bump        bump all

I was able to get this working by only bumping at step1, and not peeking or staring. The final configuration that I used (with comments) is below:

sslcrtd_program /usr/lib64/squid/ssl_crtd -s /var/lib/ssl_db -M 4MB

# Write access and cache logs to disk immediately using the stdio module.

access_log stdio:/var/log/squid/access.log
cache_log  /var/log/squid/cache.log

# Define ACLs related to ssl-bump steps.

acl step1 at_step SslBump1
acl step2 at_step SslBump2
acl step3 at_step SslBump3

# The purpose of this instance is not to cache, so disable that.

cache_store_log none
cache           deny all

# Set up http_port configuration. All clients will be explicitly specifying
# use of this proxy instance, so https_port interception is not needed.

http_access allow all
http_port   3128 ssl-bump cert=/etc/squid/certs/squid.pem \
            generate-host-certificates=on version=1

# Bump immediately at step 1. Peeking or staring at steps one or two will cause
# part or all of the TLS HELLO message to be duplicated from the client to the
# server; this includes the TLS version in use, and the purpose of this proxy
# is to upgrade TLS connections.

ssl_bump bump step1 all